{
 "metadata": {
  "name": "",
  "signature": "sha256:316f1dafb7c84a48a7d00ae2b4f8bb356ac223eca3123d067cfab9fda8aa06f6"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "from IPython.display import Image\n",
      "from IPython.html.widgets import interact"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Image('Lighthouse_schematic.jpg',width=500)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "jpeg": "/9j/4AAQSkZJRgABAQECWAJYAAD/2wBDAAMCAgMCAgMDAwMEAwMEBQgFBQQEBQoHBwYIDAoMDAsK\nCwsNDhIQDQ4RDgsLEBYQERMUFRUVDA8XGBYUGBIUFRT/2wBDAQMEBAUEBQkFBQkUDQsNFBQUFBQU\nFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBT/wAARCAGnAxUDASIA\nAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQA\nAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3\nODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWm\np6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEA\nAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSEx\nBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElK\nU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3\nuLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD9U6KK\nKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiim713bc84zQA6imq4YZB46Uz\n7RGH2bvmxnGKAJaKaJFY4B/SjeMgZ5PSgB1FNLqucnpRvXnnpQA6imrIrgkGk81cZzx9KAH0U0MC\nM54o8xcZzQA6ikDAnAPNN81CCc9KAH0U0Op7+3NCuHGQcigB1FFFABRRRQAUUUUAFFFFABRRRQAU\nUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRR\nRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFF\nABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFZ2rX50zS7y5WMO0ELzCLO3O0E4z+FaN\nYXi1W/4RjVhJtC/ZJjuBwPuNjrQBynwN+KTfGHwX/wAJE9j/AGcPtk9p9n83zAPLcrnOBjp6VNdX\nnjZfi1bQ29rp0nw8bTEae7efbci+MkoIC7Dldog/i7nj14X9jPP/AApC3yF51G8YqvVj5hzWJ468\nUahov7WqLaO86weCftUVmGBWR1kviCR3OVA49KAPoxnKyBQ7bWOwrjJDdQSfTANeb/F34y/8K01X\nwZYppq6h/wAJHqSWCzG48sQqzxoXB2nOPMzjjp1r52+GfwK8J/Hr4Ya/4/8AGeoXWpeK9QvbzdqU\nV35DaaIp5I0ijUjC7FVUO8NkrmuF8Rae/wAQP2b/ANlnT7vVLyOPVprGCa+gIW5KyS26sQWUjJBO\nfloA/QlHDu7iM/Lhd/XeMZ4Pfn+VebfDr4wf8J/8QfH3hptMe0Xw3PBbrOk5lFz5jTqxA2jbjyR3\nP3q8Uj+HOh/AH9pXwJong6GWx0rxDYzWuqW8kzSC44dzIxY8MWjXpjvxVL9mH4P+ENH/AGm/jXqU\nOgR215pl/bPZy+bLviEkt2WO0tyG2Jjj+GgD3r4IfFqX4uWviq6awGnrpOqNpkZEnmeYqxRvu6Dv\nIR+FelKHRd7yBkABBHyivgP4G/s5+E/ibZ/FzxP4oe91mW01i4gsLQzmOKzKWsMgkUKAS+5j1JGM\ncVtweNde8Qfsx+ANBn1qbTLHV/Fn/CL3utLIiSw2KmdBhmyA+Ik+Ygjg5HNAH3CyMcg7cdSuOPxN\nKVDN/d4yNjc//qr488Z/DTRP2aPH3w31f4deZp0up6kmm3+ktM8y38bsqNKUYlgyLIzHBA+Ucevq\nfwh1a4k/aF+PkU9wfs9vqOkbIncYiU6VASR6KScn3NAHuCqSgZTjBzhTwafJtGEzszzleK+MIdP1\nr4t/BL4xWPh7xLaWV3J8QtSisp5LlFgvI1dNluHLAfvc7OCOvGKzfhZ4d0b4ZfGfwFp+pfD3Wfhf\nrl28yxSWuqw3thrzi2mLLIFaUx4Cs4BZDmMdc4IB9vBVKozEMqjIZxn9amjzggqFAPGD1Ffmlf8A\nhvxl8bviF8Stcvvh8/juz0/xFqGmWbza1b2f9nwQ3MsaNHG08bK5VV5kBB28DrX2p+yrbeKbL4Ja\nDa+MLq3vdYgVkM9vcxXG5M5G6SJmRmGSPlPYUAeuUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUU\nAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQA\nUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABR\nRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAVTv9Oj1KyntLgb4J0aN1z2Ix1q5RQB812v7FVjpM\nt2NI8deKNJtJbiW4itLTU7lIoS7FiAolAxyO3avTvDXwP0Pw7r+na/JJcajrljpo0tL+8leWR4Q0\nrfNuY55mfrXo1IwDKQeQRigD4J/aJ8KeBPB/jDxBoGnaZ49h1PUsXX9k6Dey2+nanI4DP5YS4XZ8\nzkthBls9ete+fCT9newt/gv8KtB8TwGbVPBlvbNbyxyuAJomVs44yMovWvcIkBTYm2LGQQpyce3p\nUtoAsWFACg/KAOAKAOS8R/CvRPEvjXQfFN5C76nou77IQ7BVLBlJKg4bh24Irn9Q+A2k3PxXi8dW\nd7faVrDCD7etpcyJDqAiJMYljDBONz84Od5r1FjhTzj3qhq+qWugabdahezC3s7aMyyyscAKBkn9\nKAOW8IfCrQvBdprlnpVqbS21m6e6uULltztEsbYyeAVQVmN+zx4Jl+Hc/geXSvO8Py3Et2IXlcyR\nSyMzM6SZ3K2XbBBBGeK+c/GP/BV74NeGvGUGiRT3OqWYIju9RhR/Lt2yeg2HzB93lTjk+hr6n+Fv\nxP8ADXxd8LWvibwpqKaro96CYp41Ixg4II7H2PpQBwHw+/ZV0LwV4pg8R3uq6t4n1a0ytnLrOoT3\nKwAggsiyOwViCckDJwOeKm+IX7LWgePfFl54kTVdZ0DVdRCJqLaTqVxbpdqiKib1SRQSFRBnGcCv\na6KAPHdH/ZT8A6B8MdU8B2Fhc2+g318+pFY72ZZY7lsfvEkDb0YFQQVIIIyKz/Af7KGg+DfFWl+I\nLvW9d8S3+lF20/8AtjVLm5S2LKyEhJJGBba7DdjODivcqKAPC/Gv7JPhjxZ4m1LXLTUdY8OXWqOX\n1GPR9SuLaK7JJJd445FXeSzHdjPzHmvVvA/grSfh34YsvD+h232TTLNdkMe4scZySSeScnvW9RQA\nUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABR\nRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFF\nFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUU\nAFFFFADQig5AAP0pQABgDApaKAGS/cOCR9BXgH7dFv4mu/2YvHsPhmcW9+dMuWlKYLNbCJ/NAJBw\nxGMEYI7EV9AtnacdaytfWzn0W8j1RYJtPaB0uY7hQ0Txkc7weNuM5zQB/LvIjRSvvDLKrlW3cgeu\na/ZH/gjPZ+I4Pgx4nn1Bi3hue9jGk7mzgqZhPgem7HWvnDVv2V/DPxT8f6R4itdJTRrXxdNqWoWG\nmadCFto4LW0nKIIlABLzWrZIxw/Q45+pv2avGyfs0+E/C9zOTH8LNeiSGdmOyPw/q2AbmJz93yzL\n5/J2bPLAIOeAD72oqH7RkjC7h7H8qloAWiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAK\nKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAoo\nooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiii\ngAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAa+NpycCvNf2g/CHiHx58L\nNe8O+GZRb6hrEDafJPuCmKGRWV3BPcZyP5V6ZRQB8m+JPC9r4J/af/Z/8P2MCw2NtZ30QQcjP2G9\nLD8Tk/jXcfDz4Bvos3xP8PeIIItR8E65qJ1DTraUghWnaWW5HHzD55AB046VjfFn/k834J/9c7//\nANIb2vo8sFJz3OKAPmL4P+K9Y+A3jeH4VeOb+W90y8O7wv4guACZ4uR9lmZQAJFKFskLu81QCTwP\nqAMM4BGetcB8W/hXpvxb8F3Okaiot7sgyWd+BmWxuRgxzRngqysFIIIPy9a88/Z8+KurJrVx8LvH\nr+X490OFmW6kPGq2YZRHPGTgn5ZIQ5/vk8nqQD6CBB6HNLUcK7Mjjb/Dj0qSgAooooAKKKKACiii\ngAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKA\nCiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAK\nKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAoo\nooAKKKKAPmr4tbv+GzPgnjH3L8Z9P9BvetfQep6xaaNp9xqGoXEdnZW4LzTSnaqKO5J6CuA8ZfCy\nTxJ8avAvjJZ4Yk0A3AaIsQ7+Zbzx5Axg/wCt9e1eWft2+ItTuPAfh/wZoUV1daj4o1qLT57S1wrz\nWhSQSKpyMEt5fQj6igD0L4b/ALT/AIK+KfiT+xNDub43wjE8I1CwntFuoju/eRNKiiQDa33SelM+\nPvwYPxT0iDUNHuZNG8baHMLrSNWgwNj7WBVgR8yFXYEAg5xzxivCvhzq/iTxb+1p4N03V/BUXg4e\nF9EluPIgIZfImS4jjU+29Hx719otuJzlRnoR1BoA8s+AnxsHxR0vULHVbRdI8a6Owt9Y0bDJ5U3I\nLR7s5jZlYBgWHy9TXqxnIbaQAcZz/TFeC/HH4Waxo+sW/wAUvASpF4s0ZHkvbFSVTV7MYZ4WGCGl\nCq4QkDmQ5ZetegfCn4p6R8X/AAfYa/pLOkcxaKeC5AWa3kQkOhAJGdyk9eh/CgD0CimtIqruJwPW\nlBB6UALRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQA\nUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABR\nRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFF\nFABRRRQAUUUUAFFFFABRRRQBwPiyLQH+JnhJruW5XxCvnf2eiD90w8mXfv4/ueZjkc4rh/2j/hj4\nn8Vaj4M8V+ELW21HX/DGoC4TTLuZYUuosHcokPCMSEw2Djng16jrP9qDxVoy22l2t1pztJ9qvJP9\nbbARuVK855YKvHZjW425AXfbu4IxnmgDxX4FfC3WfCN54k8YeNL6HUPGPiObzbsQsPIsrZQDHDHy\n2VV/MbOcHeeK+YPhr+2KPBfxF+KV1q+seJfG9odZFnpOh2jSagLSBQEmmKxq2xBMhXkADzAM56/d\nHj3TNR1LwF4ksdHKRaxcabcw2nZfOaJhGcnphiK+FPhn+xr8W/gV4iN94Ql0ae78TWEiavd34Ey2\nVy1xHKZEDKcnajLjBX5ycZwQAfoJY3Iv7KOYRukcq5VLhCjjP8LKeQfY185fFTwrffs+eMbn4peE\n7OXUfDd66L4p8OwofnGAi3ce0HDLthz8p+VW5A5H0HqOrWXh3Snl1G/SK3ijZjNNwxVRliABycdA\nOa8x1PW9d+NMMumaHDJpPhGYGK61eaNfNu0/iWFHBxk/KS6rwGIOdpoA9I8JeMdK8eeGLLxBoV1D\nqWlX8EdxbXEEgYSKyhgOM4OCOK3ocCMYGF7Cvkq1sJv2KvE9rbQm4m+DeryCIMCZZNDuCcqxz8xi\nIZyfvY8sdM8/Vtlcrd20c1vLFNbuoZJEOQQfegC3RUCuwI5Lndgg9qnoAKKKKACiiigAooooAKKK\nKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAoooo\nAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigA\nooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooA4vxCLMe\nPvDYl8UtplyWlMei+cV/tD9zJwF3DO3l+h+5+I6maSKG3kMz7IlXLvI3C15/8S/Buh+NvFXhyw1/\nwg+uW7vL5Wpm42JZEQyE5VWDfMBt78vUEf7Ovw8VkVvDUZWMfIWuZjx+D/zoA0b/AOOPge1E8MXi\nOyvr5BkafZXCSXLn0VAck1iN8QfGPiyEQeE/Cl1YW8h51PxCzW7xDuREUO/noNw4r0HTPDWmaXbJ\nFbWcEcMY/dZj5X8TzWmd6ABQGXucjFAHnelfBuO8v01Hxbq8/jC9jlEsaXAKWUZzkFLYs6qQRnIP\np6V6GLXyFVYFWPAwABhQPp+lTIMDtj0FPoAxfEfhaw8YaFe6PrVpDf6bewtBcWs6CRJEYYZSCMEY\n4wetfOnwv8Qar+zf45t/hX40v5b3wxqcjP4W8QXTkDG0n7G7MTmQNGxA3dJUGB3+pa4T4y/C7Svi\n74KvdA1YMqSBXguI+JLedWDxSIcHBDqp6EcUAdqnLcr6HJ69O9TV8+fAD4navo+tTfCvx8wg8V6O\nm2xvHGE1a1BASVGBKlwrRhxkHcThQAQPoOgAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKK\nKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAoooo\nAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigA\nooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigDndWsNbm8TaVc2WrRW2lwmT7bYNAr\nNOpjYIQ5GVw5U8dl963YFbaC2MkDhegrh/FkHhyT4l+EX1HT7mTXUM5069itXeOMmGUOHkClU+Tf\njJHJHrXcQBBnbknAyx/i/HvQBIQD1GaNoxjAxS0UAIAAMAYFLRRQAVFOVRCzZ7AkfWpajeMmQOpw\ncYOfSgDyb4/fBP8A4WzoVpc6Vd/2J4t0iX7TpOsQko8TYbKEryUOcleQSoOOBVf9n741XPxV0a+0\nzXbJtH8baFN9m1nSy3McmBh0xjMZO4AkD7p4r2Jo+c7m+navAP2gPhXrE2paf8SfAybPHPh+IOLQ\nDA1K0U7ntmPGSV8wLg8GQnB6UAfQEbFkBIwadXB/Bv4q6b8WvA9rrdkfKuAWivLFz++tZ1dkdHXA\nK/MpxkcjBHBBruUYt1XA+tAD6KKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKK\nACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooA\nKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAo\noooAKKKKACiiigAooooAKKKKACiiigDm9al12PxRo4tLTT59GYyC7mndhcQ4jcgxgDBydoOT0Jrd\nt9pwwGMrwMn/APVXG+KP7Ab4heFhfa1dW2tBp/sGmxXe2Oc+RLvLRfxYTeQfVR6V2FnwGB+Vv7me\ng7HHbNAFmiiigAooooAKKKKAGyNtQnOMd6gkVj8zADj5R3B/zirNFAHzB8XfCesfArxxJ8V/BFuZ\nNJn2p4o0OE5W4jwFE0SHhZAViztK5G8nJJz9BeDPF+l+PPDlhr+i3K3Wl30CTwyjurKCOOxwehrS\nuLZZmdJQJonHMb9AMYP4Yz+dfK2prN+yH8R2vrRS3wg8S3hkvYol2Q6DcM+fNJGVWB/MYkkKFEPU\n9gD6zyKWs23ure8tYL6CZZrWVQ0TqRs2noQenOetaCfcXGcY70AOooooAKKKKACiiigAooooAKKK\nKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAoooo\nAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigA\nooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooA5jWby/j8YaLBbaILyzk8z7V\nqZMYNkBG5UgEhjuYKvyg/f8Aqa6C3+XjGc5JYetcx4jtpX8ZeHpl8QDT4Y2mLaXs5vz5Mg2ltwIC\n5D9Dyn4109qWaNWJBUqMYOe3r3oAnooooAKKKKACiiigAooooAjlhEykFiAfSsvxF4Z03xJol7pW\npWUd/p97G0NxbSdJEYEMPbgnpWxUcy74yvzANwShwR+PagD5b8Aa9qX7Nfj2y+G3im6e+8F6hI8n\nhjWp/m8hmDM1nMwxggrIwZhj50G4nivqFbmMRk7xhQCSMkfhXHfFP4Y6X8WPBuoeG9YtlaGYK1vc\nquXgkVldJEbqrBlHQ9uvNeUfAz4lat4T8TzfCTx/O83iXTYz/ZGpzn5dYs1IVGy3LSKrRb/vfMx5\nPUgH0arbieMAcU6oopC7Nggr2xT2kVSASAScAUAOooooAKKKKACiiigAooooAKKKKACiiigAoooo\nAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigA\nooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACi\niigAooooAKKKKACiiigAooooAKKKKACiiigDg/Fk2kr8RfCa3Oiy32r7pvsd+sLsll+5l3MzAbRu\nXcnJ6sK7aIbmDHG4Ag85x7U13Mc2MAs3QkdvT+ZogGZCe3PUY/DigCxRRRQAUUUUAFFFFABRRRQA\nUUUUAFeVfHj4K2nxi8OxxwXsmi+JLCYXWla1bgb7ScAhWOQcrzyPYc16rTDEpzx16igDxj9n742T\nfEm0vvD/AIrs00P4gaJL5GpaXyqyYAInhyTujOSMhm5Rua9kB3N03J2Poa8P/aB+C99qmoWfxG8D\nOmnePdBTzFwzImpW6ks9tIACCWVpFUlTgvnI6jrvgp8ZNN+L/g2DVrZJLS/jdrW/0+YBZLe5VmV0\nwCRgMjYOeRg8ZxQB6RRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUA\nFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAU\nUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRR\nRQAUUUUAITgUZpJGKoSBk+lcl8UPGA+HXw78T+J2HmLo+nz3xB5+WNGY/wAqAPE/F/jfxp8cviZq\nnhDwDrZ8M+FdBKw6t4jt0Z5HuyA3kROGULhXhJPzcEjA61vfszeJvEv/AAlPxE8D+I9eTxSfCtza\npb6yFIedZ1kco5LNl02hTz1zwOleKR/Cn4s+Hv2YNJ1T4feLZPDmvN52q69ALa3ma/VpG3FTLE+J\nBAExgqPkHvXvn7JWjeHLP4S6Vqnh37RM+rxi81K6vSTdTXjfNOZskgMJGf5U+QchRjFAHtlFFFAB\nRRRQAUUUUAFFFFABRRRQAUUUUAQ3ChlA6nkhfU182fGjwZrfwf8AGz/F/wAB2MupSuqW/iXw9ApJ\nvrfauJkC8+ahjiUHDfKX49PpSdgihi21RwTjJ5qCSJZkZZF8xHTbvIBBB7EUAZngrx1ofxD8MWXi\nDQNQh1HS7xA8U0LhuoBwcHg8jjrzW8DkV8s6zY3n7Jnj3+3NMieT4S67dKdVhT5zo0zPgTIp+byi\nHywGcCLgDv8ATGiX9tqumwXtnOl1bXCiWOeNsq6noRQBfooooAKKKKACiiigAooooAKKKKACiiig\nAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAC\niiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKK\nKKACiiigAooooAKKKKACiiigAooooARhlSM496+ef25r+9g/Z213R7D5bnxGy+H4WD7Tm5V4xn16\njivoSbiM8E/TrXmHx2+G178SrTwha28lslrp3iOw1W8SdWJlhgk3Mi4PDEEgE8UAeG+F/ix8U/DP\nwstvA2p/C7xBq/i/7IbJNZijlbTmDjCyvN5RChFOdvOdvUZ499/Z/wDh5dfC/wCGOk6Hf3SXuohP\ntN7cRj5GuZPnlC8n5Q5bHtXeRxRx5AOwAABB/n0qSKERzs6rjcBz/KgCeiiigAooooAKKKKACiii\ngAooooAKKKKACmqoQYUAD0FOooAxNZ0Ky8SaVd6XqECXNjeQyW9zbygSRyI6lWQg8EYJGPevnDwB\nrV7+yx45tfAGv3MjfDrWJ3Ph7W7klY7OVtztaSFsgZYSlfmH3lG3vX1IscijaCgXPYHOP8a5T4k/\nDnR/iZ4U1Lw/rNv9struMfu87SjhgUkB7MrAH8OlAHVRlnclty88L/X8anr5s+A/xB1v4feK3+Ef\nxEuSdSsEWPw7q0mMazbKdgLEZAlVfJ3A7MmQ4Xg4+jRcq2NoLA9+n86AJqKRSWGSNp9KWgAooooA\nKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAo\noooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACii\nigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAEPANQhysJZ+TjcKnooA5jWtcv7LxZot\nhDpL3FldbzLfg/LBiNyAfqVA/wCBV0cTlie64GG9a5jxBb3MnjXw9JF4gi0+3jMvm6WzANffupAA\nBnJ2nD8A/crp07dhj7tAElFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABVe4BZgqjtyR1/zmrF\nFAHk/wAc/gxa/GDwwsccraT4l09zPpWuQZ82zuMcMGBB2hgpIzg7RxxWL+z38Y7/AMbJqXhLxZGN\nP8feHiYtQtyAFnXAKXEfAyh3YyQPmRuO59xIyCM49xXhn7QXwivPE7ad468Lf6J8QvDf7zT5ccXc\nGT5lu44O0o8oGCMM+eRxQB7jCSYkyQxwMkd6fXlvwV+MFl8YvCrXaqbLW7J/s+q6Y2RNZXKkq6lS\nM4LK204wRggnOa9KhAjkwW+ZyeB6/wCNAFiiiigAooooAKKKKACiiigAooooAKKKKACiiigAoooo\nAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigA\nooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACi\niigAooooAKKKKAOH8TS6R/wsTwqt7o95dapvmFjfRNiKBvJkLFhvGcpvUZU8sPqO0QgkZ+9jv1rn\ndXj8R/8ACW6O1hLa/wBiEyfbhJF+8VfLfZtOf7+zt0zXRr1XPJx1FAD6KKKACiiigAooooAKKKKA\nCiiigAooooAKKKKACiiigBDUJtch/nO5j970HpU9FAHzZ8cPAOt/CjxQfi38O7USXUabfEGgxHC6\npCAMOqngSrsUAgrkMxJzXs/w6+IWh/EzwrYeJdBuDdadeoGjkIwwzzhh2PIz9a6SaNjJvA6DaPoe\n/wClfLXiLRb79k3x5P4y0G3mf4X63OP7b0aJCsemSltv21ccKhDLvyo2rDktjoAfVJdsDGN3Xn0p\n4ORkdKztH1yz8QaVbahp80V3aXMSzQyxOGV0YA5BHBHNaC7VUAYAxwKAHUUUUAFFFFABRRRQAUUU\nUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQ\nAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAB\nRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAHDeJ18OH4i+Fv7QvLiHX8zHToo1lKSfuJd4YqNnC72+cj\nkD2rtIgFONxc4GWPeuY1651aPxnoEVtoNrf6VI0v2nUJJcS2h8pyCq7DncQqZ3D7x+h6iLnGF2KA\nML0/SgCSiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACqOt6Va67pN3p19bx3dld\nRtDNBL92RGGGX8QTV6myAbTnGPegD5U8Na5c/sneP4/BuqzSXPwr1qZm0TUpcu+lXDkyPbSsOdjP\n57KSDgFBuHSvqeORbiNSOpGcZzXK/EXwDofxG8L3uga7ZQ3enXyje0kYYrICCr5PcYGD1ryD4MfE\nHWfhp4zHwj8eXElzfhCfDOvXEhb+1bVPlKuW5MqAxbjlixl5PqAfRqk5wadUUTsxIZSCOpxwfpUt\nABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUA\nFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAU\nUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQBx/iG3jk8ceH3/AOEmk02ZfNI0cSoq\nX6+VIACpXcxU/P8AKR9z2NdVCOcFgzgAMo6A+1cn4kksx468NrceH7i9vS0v2TVo4I2jsj5Mm7e5\nYMu5dy8A/fHqcdVa459e5x1/HvigCxRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFF\nABTJd/lny9u7sG6U+igCFUKg4XGRkj3rzX46/B7TPjH4Rk0yWabTdatZBdaRqdvxLZ3Y5jlBIIID\nhSeP4RXqFV3SMsc7twz3559KAPFf2fvjNfa9c3vgXxykelfELRBsnt+Vjv4cArcQ5JyCDggMfmR+\ng4Ht7TIoyT2zjvivDvj58GLnxilv4v8ACN1HpXj/AMP4ewvjkGVMnfbSYB3K6PIBkHDOCMEAjofg\nb8YbT4ueFXle3bTPE+lsLLWdJuMB7S8TKSKME5Tej7T1IAJAPFAHqdFFFABRRRQAUUUUAFFFFABR\nRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFF\nFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUU\nAFFFFABRRRQAUUUUAFFFFAHL63Hqr+LdEaHWrOy0pGl+0WEsJMt5+6fCo+8AbTtcjaeFPTqOit8Y\nwhJQdMjr6YPpXFeKR4cb4j+ExqFvNLr5af8As6RJJRHEfIl3lgp2HKbx84PUY5xXaQcEZGHI5H0/\nSgCeiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAppRWBBAIPUU6igCOQhE\n9PQCvm346/DDX/B3i+L4ufDi1a78R2qeXq2iRqSdYtQASoC8+YCigHDffPFfScqF1+XAYdCe1RR2\nxQ7s5kOAz/3se3QfhQByvwy+JOjfFfwha+IvD14LmyuOWUnLQvxujcdVYDB2nBG4HvXXRdD8xJ7g\nnOK+XfHeial+zF4/k8eeG4Wk+HeryofEmiwfMLWYtsN5EDyBgxblU42xEhck5+jfDuu2OuaNa6pp\n9yL+yvo1nguExiRWGR9MA45x05oA2aKjE6M4QHkjIqSgAooooAKKKKACiiigAooooAKKKKACiiig\nAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAC\niiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKK\nKKAOa1qTXYvFGjrYWtu+jyGT+0biSbEiKI32BE2/Md4TPI4J9K3rYkqMrgYByRjOevHauP8AENrp\ncvxF8MzXWsXNnqkZmFpYR48u5Bhk3bvlPQFj1HKj6Hr4fmlbLNuTgocY9j+NAFiiiigAooooAKKK\nKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAMe/wBJt9WsprG9hE9nOjQy20q7\nkdCOVIPBByQfUcV806bqF3+yZ8Qo9E1W4kHwl165b+zr6QlYNEunzIYZCflWJj55HKgHYMHrX1dX\nOePfBWkfELw1eaBr1ot5pF2m2eFv4/QZHI5549KANnJMiZ6A8cYIz0FWq+Yfgr431z4MeMj8JviB\neGe3LAeFddnGft0GSohkZeBIuE+8FyZBjODj6YUts9G6jHegCaimRv5iA4x7U+gAooooAKKKKACi\niigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKK\nKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAMzxH4i0/wnot1q2qXMdnp9qnmT\nzynCovr/ACrwHT/29vhtdy2jTxaxp+mXEojXWLq3jWyUEgBi4kJwc+lem/Hz4UWvxr+Fuu+D7ud7\nSLUYdi3CEZicEEEZHsfzrxzVfjR8QPAGly23xf8Ah3BfeFpVkhvvEmgybraK3K4laS1DSyqm0kkk\ngAZ54NAH05a6jFf2sNxautxBOiyRSIcqyMMhvoQakMzM6iNQwJ5OeAO/418jftKftF3XhDXPBfgz\nwfetothrGljVl1az0y4vnitQWVRGkXKkkL1B6niqnwf/AGota0/RvH83iZr3xPoXhbShrNtrsmj3\nWnNLEEldopjMCGkUIvKhRktxyAAD7ENzuVWiAdSfX+VPMu0jcMA9DXxf4l1r4/6f8MJPirN4t0W0\nVFjlHhlbGUwCGSVYgGYT/MwV9+QQOAMcGvq34eatc694F8N6pdMpubzTLaeYxjEe94lZsA5OMk96\nAOmXOBkAH2pabGpVFBxkegwKdQAUUUUAFFFFABRRRQAUUhOOvFIXUdWA5x170AeAfFLxDe2v7V3w\ne0eFoktLsXzzbolZmxZXZADEZGCoPFe+RR7GY5yT1OOTXzh8WSP+GzvgmM8+Vf8AH/bje19Iqw3k\nZGeuKAH0UUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAU0qC2\ne+MU6igDzz4y/B7T/i54Pl066cWur2wa40rVYox51hdqN0MyEEH5XVGK5Abbg1xn7PvxY1O+1G/+\nHXjWP7P480GLdKQ+5b22ypS4QkA4w6A8cMCMnGT7o/KNxu46eteL/tAfBST4i6XZ6/oF9Jo/jnRJ\nBdaZfoPvEAhoXHUoys44I5IOcDFAHsscysAOQcA4NOD4KgjBPSvLPgP8ao/i3oFxBqNqukeLNKIt\nta0knDW1wMq+FPOwsj7W5DBcgnrXodrr+mXGqTaWmo2kuqW6CSWzSdTNGhOAzJnIBPGSKANOikJA\n6nFLQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAF\nFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAcz8RNB1HxT4T1\nPR9L1d9AvryAxQanCiu8EmQQQrAqeAeor598QfDL9ojx34a1Dwf4l8S+Drfw7qltLp+oanppkkvZ\nLaRCkmI3tVjDMjMOCMdiK+pXiEhUkkFTng9fY+1Na3RnDYxg5wOhPvQB86/Ef9m7Wlm8H678PNT0\n+28R+G9OTSlj1oF7a6tuSwf5JCp3ENwvbGccVf8ABXwT8U6joHjSx+JWraffv4lshYtpmhwhbS3i\nCyK2w+XGWLiQfeH8I9TXvRtYyQcYx6fy/rSvAsiFSW5755HuPegD46139nv9oDUvh7P8OIPGvhmT\nwn5kfkapcb/7QMCypL5bJ9mKZypXO48HrX1Z4K0N/DPg7QtGkkWWXT7CC0eZejtHGqlgPcj0Fbir\nt7k/WkaJWdWPVelACx42Lg7h6mnUijaAMk47mloAKKKKACiiigAooooARjhTxmsXW9f03w9bPc6j\ndLY25dUWeUfLvfOMflW0xAU56V518dfh0vxV+E/ifw0qZnvbGeO2YjJin2EIy+hBNAHlfxa3XH7Y\nfwTljUELBfMJCcDBsr3Oce3T619C6ZrtjqOqX1hb3Mc15YiPz4V+9CHGUz/vAZ/Cvhjw98XE8UfE\nv4F+J76ZTPp+m6quoWwbaVaCzv8A5Wz0O1FbkdxXvn7IOkXF/wCGvEXj+/En2/xpqUuooZQdwsxL\nIbRcnqBDIoHbHSgD6AooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKA\nCiiigAooooAbIGMbbQC2DgHpmqqlUBZSZAT90c4PfrVyo3hWQYbLA9Qeh4oA/NH9v79p7w38Afij\nbax8NdTks/ijslttTS0jWSzmiyv/AB8q+V8xSDsIQ/ekyRxn5D/Y8/a48SeE/wBqrS/FnivWrzUb\nbW5vsWptMwYOsiskXynAVVkdD8uOlfd37Z//AATH0j4v3934q+Hki6B4snaWe5tDGv2a9c/N1BXy\n2Jzyd2d3tz+RfxB+HXiz4UeKG0LxPpV9ouqWzDYl7A8TAA5DR7gMjOcEd80Af0zwXKXlrBNDKJYZ\n0Ekcg6EHkEfgauDpxXyV/wAE4/2gk+Nf7POl2d7cRN4h8NomnXcYfc4VNyQsy9dxSME/WvrUdKAF\nooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiimSOUGQCR7c0APoq\nLzHBIK8dmH+FEbuVG7HT73r+HagCWikBJ/pSM2xSxycelADqKqm5kVsFV3f3N3OP73+fSnS3Plpn\nIAxu3twAKALFFQJM7TlNvyjqTxj/ABqegAooooAKKKKACiiigAooooAKKKKACiiigAooooAjedI1\nJZgoBwSaxh478Nk4/t/TFPPDXcYPXHQmtWaNLhXSSMOh+V1kGQRXi0v7H/wnv7mW5l8MW1xJIxZ5\nCqk7icn+GgD1X/hOfDf/AEMGlf8AgbH/APFUf8J14b/6GDSvX/j9j/8Aiq8p/wCGNPhH/wBClbf9\n+0/+Jr5++K/wJ8CeMfGK/C74beGLSPWoVVtc8RmNRHpFuSSUBVSTMVVhtJXHmIcnOKAPtRPiB4Yl\nzs8R6U4Bxlb2M/8As1DfEDwwrKp8RaXlskYvIz/WvDvCH7CXwk8K+G9P0yPQIr4W8YEl5NjzJieW\nckgk7m5wT3615n8cfgz8NvD+s2vgXwH4JsdR+IGuoDFGsSGHTYicC6mwhIVcsyrjD+WwyuM0AfXq\n+P8Aww/3fEekt9L2L/4qnDx54aI/5GHSueP+P2P/AOKr5y+GX7Afw08I+HY7TVtHOs6nI3m3d1P8\nqmQ8ny1OcL24NYXx1+D/AMIfhFpum2Wn+A7fXPF+vPLDomkRwoWlmG0FyNpIVWkj3MAcbhxQB9U/\n8J94Y3sn/CR6TvUZK/bosj8N1Enj7wzEpLeIdLGBkj7ZGT+Wa+Xvg5/wT/8ABHhXRG1PxrYW+ueK\ntRYyXB2BIYVGCsSKcjC4znA5J4rR+LPwS+B3wZ8KHxNrPhKCZWlWK2gto0kubuZlZhHECBvYhWwu\neQPagD6QHj7wwWCjxFpJY84+2xZ/9Co/4T3wzu2/8JDpe70+2R5/nXyD8DP2FfD2omXxf4+8PQWu\np3ufs2g2wxDp0OP9W7bRvbLNyUHavSPHX7NXwN+HnhO/8R654ctLbT9Ni8x7p1TIUsAAGI7sQKAP\ndm8feGFYA+I9JBbgA30XP/j1KfHfhodfEGl9cf8AH5H/APFV8UfCP9jjw78XvET/ABB8UeFV8N+G\n0kV9C8PJAIZGTJZZrkAAdNnykMBhuea901T9kb4RaXZXN5ceF7KOGCBpZZVjQbVUFixO3jGOv4UA\newy+P/DEJ/eeItKTt817GP8A2alHj3wyX2DxDpe7Gf8Aj8jx+ea+FPB/7LXhX9pPxVBr0HhlfDvw\nz0x/MtWhUG5145+WYMAuIiqllOW3CQHjHP0in7HXwlEL48J2YVeSFVTyO5+X6UAetP4+8MR7t3iL\nSl29c3sfH/j1H/Ce+GT08Q6Ufpex/wDxVfCOpfs7eCv2jfiBceG/BHh6Hw/4L0e6eLV/EyQqZL2e\nMmNraB1AIw28Fg+QYsY54+jLD9jD4TWdslvH4UtRGBgtIql/l7n5eT60AewS+PPDJjP/ABUOl4Iz\n/wAfkf8AjUDeO/DUg82PxJpex8YZb2IgEfj718UfE/4CeDvHPj+5+Ffw18JwQXti8b654ieNdmmx\nsiyCNcLzIwkjOCV+Vjzxz7j4X/YY+EvhPQrPTx4dgvXtYwFmlVSZXwMkgg9SB3PWgD4e/aU0WTQf\n2wdI8I+GdQszpvii7XVoJra7jMdpC0TQ3Cbi2F3JDLwf7/uK/Tfwp4g8HeEfDemaLY69pSWWmWkV\nlEq3sbHZEgRejdcL9a/Mf9qr4E6Vof7eXww8FfDzQNPM2qeHpnezmASNZWF6Hc4U4KRrvAxyVAyM\n5H2X8Mf2A/hh8P8AwhbWWo6ZHrOrsomvL+4YZa4PLtHnJjBYtgA8celAH0OfHnhof8zDpf4Xkf8A\njTV8f+GHdkHiPSS68sv22LI/8er5T+O/wa+FPws06007Q/AUOueMdX/0bS9JhRP3zk48yUbCfLTO\n8nB4VvSr/wAHP2AvBvhzRFv/ABbpdvrfiLUFMl5IIhHHBubcIUTkEINqBuMhc4GcAA+n/wDhO/DW\n4L/wkGl5xn/j8j6fnTR8QPC5fZ/wkek7j0H22Ln6fNXzf8Xvgl8Efgz4Qm1LUvCMFxczH7LYadbq\njT307fLFDGCMkuxVcDP3h1rmPgj+wn4Xnjk8YePNAg/ta/JNroaRhbfTYf4V6YLEDcTtHLkc9SAf\nXI8d+GySB4g0vI7fbI8/zpG8e+GUIDeItJUnoDfRDP8A49Xg/j79nb4HfDHw1f8AirWtAtbaysoz\nI74QlhgttUEDk44ryT4R/sY+HPidr7+N/FXhqPRNDZjHovhsDa6RgZE052je5ZmG0qeFU7ucAA+0\nz498NAZ/4SDS+uOLyP8AxprfELwui5bxHpKjOMm9jGT7fNzXj+qfslfB/R9Knvbvw3Z2sEKmWS4M\nSLtx+HHXpXz74B/ZU8IftKeMLXxXb+GY/DXwu06QPptkIwlxqzg7vOYAALF/q8cuGww4xyAfcq+O\n/DTjK+INLI9ReR//ABVNbx/4YRdzeItKC88m9jxx1/iryGT9jX4QQIp/4RqCBFBLBQqqQBk54618\n8yfs4+CP2ifHE+jeEvDcOhfDzRLkxatrkeA+okNgw25VRtGEcMwb+NODQB9yDx/4YOf+Ki0ogDOf\ntseMfXdQfH/hhSAfEWlDIzzeR9PzryCy/Ys+EdlbJajwlaywIoTEkaElRyCfl+bnuf6V4D8TvgT4\nI+Jvjq4+Gfwx8NWlnc2xC674ne3SSLT4unlRAD5puTj5kK+WwHWgD7dXx/4YdVZfEWlMrdCt7GQf\n/HqcfHnhpeviDSx/2+R/414poP7Dfwh8M6Hb2EPhuK4S2i8vdIAzuRyGJIzuyc569K8n+MXwX8AQ\na3beAPAPgqy1Hx5eoJ5LmaNPJ0yHAzLNhGOfnQAEDO/OfUA+w4/HnhmXOzxFpT4ODtvYjg/99U3/\nAIT/AMMZ/wCRi0o+4vI8fzrwD4dfsF/CnwH4YtdMm0wa1eIwa61C7AL3M+BnJO4qCR93J61x3xx+\nEPwm+G1ra6DoXgK21nxxrX7vS9IhiQKMklppAFOxFCudwU5IA4zkAH1gvxA8MOzKviPSWZeCBexZ\nH/j1H/CfeGQQP+Eh0vJ6f6ZH/jXzT8G/2APAfhLw6sni7TrbXPE+oET386RKkMUnJ8mJefkUswBG\nMgDgdKk+L/wV+Cnwd8MHVLjwhDf6ncn7Lp2nxxI0l7KxCiJAR0+bJIB2jLYOKAPpP/hPvDG8J/wk\nek7z0X7dFk/hupW8eeGl6+IdLH/b5H/jXyN8Bf2CPDUfn+LvHmiwPr2qEzW2jouYdLhLZSLkDLBd\ngZtq5IPrXf8AxA/Z4+Bvw18JX3iTW/DllBptmu8/uoy9w/8ADEoIG5nOFC9ycUAe8f8ACwPDG5R/\nwkelAt90G9jGfp81L/wn3hnP/Iw6We2ReR4/nXxl8GP2MfDfxK8SS/ETxb4ZTQ9ClVv7C8MCIKbe\nPIQTTNhfmbDsF2nCyDnjn2fXf2U/gv4Z0K71W/8ADdjZaVYwPcXExRBFHGq5Z24AAABJNAHs0nj7\nwxCu5/EekqucZN7F/wDFUv8AwnfhrIH/AAkGl8jI/wBNj5/8er4g+Hf7J/hD9oTxZF4pfw0PDXw7\ns2ZdLsmjCz6swBBmkAACpksAMuD5YPGcD6GX9jL4TCEofC9oQoAAaND5Y/KgD1iTx/4YiBL+ItKQ\nDqWvYx/7NR/wnvhnAP8AwkOlYIyD9tjxj/vqvg60/Z48EftL+OxD4T8PwaR8LtIkEV9rJiVpdWmB\n3eVAQBhOY8uGOdzDbxz9Jw/sX/CK2s47X/hErcwxRKql0XgAAAE7etAHr48d+Gim7/hIdLC4zk3k\nY4/76po+IHhhk3jxFpRXOMi8jP8AWvh/4h/AjwZ8UviJJ8Ofh54XgsLfT7nyfEnihkV47OPdhreL\nC/65lWQfeUoSpGc8e+eHP2IfhNoOj2tn/wAI7BdGFMNczopaQ+pyD/OgD2NvHXhtpdh8QaXgj/n9\niwf/AB6vGv2gvg18H/2kvDF1pnii+0aS827bXU7e/jSe2cHIIYNgn2bPWvF/jh8GPAVz4oX4XfDn\nwjZS+OLuNZbrUfJTytGhkGFmkIUkscllU7d3lt8wxXqfgH9gr4UeDfClnpV3oUOszAl5rm7RZHll\nIwzjcCemB16CgD40/Z/8B6z+wD+0xBa3mv6brfw48Tn7EuqxXcciwuSrxvKqkMGVVcE7duSfUV+o\ndr4/8LyxqE8SaS5A5Av4if0avgr9v34Y/CL4O/BbV7DTvCUc/iq+s3NnHZxput4kwDcPgZCKSint\nlxW9+xB+xn8NdZ/Zw8G+KtX006trGvWcd7PPMAfLLAAoM5449uvSgD7c/wCE88Nf9DDpX/gbH/8A\nFU3/AIWB4X3bf+Ej0rd/d+2x5/8AQq+Zfjh8F/gj8G/Cy3914Lh1G/vJls9P0qzgjaa8uGUsAox1\n2qxOAeFNZHwR/YM8M29veeJfHmk2k/iPVVWR9Ht1Bg06Ntx8gEgbvvFS21c7RkdqAPrIePfDR/5m\nDS8Zxn7ZH/jSH4geGAwU+I9KDE4AN7GD/wChV8+/FD9nz4HfCvwXfeIdb8NwLY2qoqxIE3TOzqqI\noI+YlmUCvOfgv+xL4e8d63N4/wDHPh6PRrG4AbR/DflBDbWzHKG44GZSgTKlTsO4AnrQB9lf8J34\nayR/wkGl5HJ/0yP/ABph+IPhdc7vEekrju17GB+e6vGdf/ZT+DHhbQNQ1fU/DtpbWNpC9zOzhSoR\nFLHGRjoK8N+HP7Jfhj4/eL18YX3hW38O/De0yNF0lYwkuoHIHnzAKAEbDsB8wYOrZFAH23/wnfhr\n/oYNL/8AAyP/ABpr/EDwwgy3iLSlHqbyPH868ku/2OvhDbWctxL4Zt7eGNDI0hCoI1UZznHGPXtX\nznpn7Nngv9pPx01p4b8Pf8I78MNIuCtxqYjCy6tOowY7d1A2oGJ3OGOWjYFeSQAfdA8eeGjjHiHS\nznuLyMj/ANCobx54aQAt4g0sA9zeR4/nXkcP7GPwl0+0WGPwpa+QiBQGRcnA6s23k18/eMPgJ4M+\nNHjq58A/Dvw1DYaDYTKviHxOFGxCAJPIgKry5/dgncpAkzzjBAPt1fHvhl03L4i0ll9VvYiP/QqV\nvHnhpVDHxBpeD0P2yP8AxrxnSf2IPhFomiWmnw+FoJ44IVj80opkYAAbycZLnqT1JJOa8P8Ai98G\nPAes+MV+Ffw38I29z4nljD6prCxq9toNuxK+Y4Cn5yEk2oduSo+YZ4APtf8A4Trw3/0MGlc/9Psf\n/wAVSf8ACeeGv+hh0v1/4/I/8a8J8I/sKfC3wv4a03T7zRhrFxbJmXULkBpJ3OS3XJAyxwMnAAHa\nvP8A46/Bj4ZeDhYeFPCPgK313x/roeKwtAF8u1A2qbichGIRC6t90ggN0oA+tv8AhPPDX/Qw6V0z\n/wAfsf8A8VSDx74aOceIdLOOT/pkfH6187fDD9hH4eeE/CNhaa5YxeI9YlZpbm7mjARnOTsRTu2K\nowMDglc4BNY/xo+Dfwb+EOhQzf8ACCJrOt6lL9j03RbIKJtQnPSPAXJUnAJweo4OaAPqJvHnhpcZ\n8Q6Vzx/x+x//ABVA8d+GixA8Q6VkdR9tj/8Aiq+W/gd+wj4V0bTb3V/HWnW+qeI9TmM5so4wtrp0\nZVQII1IwSCGYsFUnfjHGTvfFL4BfAj4T+ELzxNr/AIatYLGDChbeOPzbiTBwiLgZfg984BoA+hf+\nE+8M4z/wkOlYzjP22P8Axo/4T3wzgH/hIdLAPQm8jH9a+Rfgd+xRomv3OoeM/H/hu30n7cCmneE4\nkBh0y3wf9dlVDy/Ng5QY2Dk549L8WfssfBTwt4cvdT1fw7Z22l2cYnluJwiqqggBQSOMkjA9TQB7\ngfHfhoEA+IdLBPTN7Hz/AOPUHx34bAyfEGlj63kf+NfF3wq/ZR8M/HPxa/jfU/DJ8M+AIkx4f0YR\niOW+jfkXUrALtyqxlVw4+Zvm4598i/Y0+FBOZPCdqykYxIqt/NaAPVh458Nkf8jBpX/gbH/8VUU/\njXw1Jgf8JFpiNg4IvYuD69a8uH7GfwiAx/wiVrx6Rpj/ANBoP7G3whUEt4StMdfmjT/4mgDlfEWv\n/FTwR4i1DVfD3j3wt430OZsx6LrNzDFcwjjiNo/LU9D99jwag8N/t2eC7PXYtC8eQyeAddmYJ5V3\nIl3DK2cYWS3aVF5/vMOtebeJPAnw4utavdC8DfBW/wDFWq203kvqV1bLbaVEccg3SpIQc4GNnY+l\nZ9l/wTeX4jXCy/ECfSdG0lXDP4c8PWau4GckfbB5be2dnvQB9zeG/EGm+JbD7bpOo22pWTn5JLaU\nOBx0JHf61qkgAk9K4T4NfBjwr8C/CK+HPCOnf2dpYcybWO53YjlmbqT7mu6kOEY8njtQB8l/Gz4W\n+K/iTafEfxJ421S80LwzoVlcnQtMsLhU80RQGVbqVo8tnexG3cB+6GVwTn52+DXw4+PP7VH7Nmj6\nzafEM6CbC6ZdIEyKBdwxtJGXmxGWLAgbegIJyCcV1/jT48fG349/Cj4ieCdP+G994Y14y3CPqdy7\nrbw2aRJIUDCMeZJKFkjAOP8AWLyeldD+zZ8UPFs/wl+Hnw58DeF9W0TXLFQusapqVhm2soxuEn+8\nxdkIQ7eMnPHIB9r+G7a+stMs7bUrz7ffQxBZrrAHnN3OAAB+QFbFVYECznnLDgYXGB2BPerVABRR\nRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQA1o1ZgxGSOhpcYpaKACs+O0jhLyJAiyMcvsGM+57mt\nCvA/jl8V/GelePPC3w/8DR2Ftr3iBJZE1bV22W8Sxq7uFwj7m2xtgFcZI59AD3ESL5ZKjcwGdq8Z\n/A02G3iWUyeUol3bfMYDew9c14l4Gl+N3hfxxY2Pi46P4p8PXnD6pp/7u4tm4+9GIUXZ153E/d45\nONL4c/HO11e68c/8JLdQaauieKr3RLR2YASRxCLb265f/wCvQB7PtGc49qjktYZXR3iR3T7rMuSv\n0PaoYtTt5bVblZB5LDduzxjGc/lWdoXjbRPE091DpWow301qQs8cTZMZOcA/98n8qANoIozgdajm\ns4LhcSwpIAdwDLnB9aydb8a6J4bt2n1TUIbGFHWNnlbAViQAD9SQPxpms+PNB8P2Md7qOpw2tnJt\n2zyH5TuG5fzGTQBueUuc7ec5ps1rDcRNFLGskbfeRhkGoLLVbfUYVltm82MjhlwRn0+tWkkV84PI\n6j0oARYkVVUKAq8ADtStGrIUKgqRgg9xTqKAIYLSG1hSKGJYo0ACogwBintErMrFQSvQ0+igCGK0\nggDiOJIw5ywVcZPrUjxq4wwyKdRQBElrDG7usSK74LMBgtgY5P4VIFAOcc0tNLgNjmgD4M+NKbP+\nCt3wFUJwfC16cjp/qNUxn8a+741DMGbmTaAfQeuK8e8X/s3aP4p/aW8G/Ga51GeDVvDGny6bDZgf\nupUkS4UsTnr/AKS3bsK9ijIY5xjjj3oAR7OCR1doUZ16MRyPoaeIlAAA4ByPrT6KAIZ7SG5KmWJJ\nNpyu9c4PqKesSoSQuCetPooAje3ilQo8auh6qwyDThGo6KB24p1FADGhRjllB4xz6U2G2it1CxRr\nGo6BRgCpaKAGSRJKhR1DKeoNRwWUFtEI4oUjQdFQYFT0UARrBGm3CgbTke1MSyt4zIUhRGkOXKjB\nb61PRQA0RqoAAxjpUX2G388z+SnnEbTJj5iPTP4Cp6KAIxBGHLBRuIAJpn2K3+0faPJQzYx5hGTj\n61PRQA0xqSDjkVHJZwS7d8SPt+7uGcfSpqKAGNEjAArkDpTLi0hulCzRJKoOQrjIzU1FADPKQYwo\nAAwAPSmXFnBdRGOaNZIzyVboamooAjS3ijj8tY1VP7qjAFKsSIchcHpT6KAIYLOC1jWOGFIkXoqL\ngCpNo9KdRQBXhsLeBy8cKIzEsSowST1JqbYuQcdOlOooAiW1hWZ5hEglcAM4UbiB05p7LlSB+lOp\nsmNh3Zx7UAfPX7eNrDL+yR8UpJ4wsiaHMBJgFlGV7+/FX/2FMv8Asf8AwnLDDHQoc/rXoHxe+Gdn\n8Yvhp4h8FahNJaWGt2xs7iVRlwh9Ofb1FSfCD4c2fwa+F/hrwVY3Mt7ZaHZpZx3EowzqvcjJ9fWg\nDrprOC4MZliSQxtuQsudpxjI/M1IUU54HNAcEgZ5Iz+FOoAgmsbe4t/IlhSSLIOxxkdc/wA6kWJE\nXaqgL6U+igCOW3jnieORFeNwQysMg0QwR28SRxoqRoMKqjAAqSigCMwRkOCoIfhge9JHbRQoEjjW\nNB0VRgVLRQA0RqNvH3RgVHFZwQj93CkfO75RjJ9amooAQKAMY4qBbC2WcTLAiygEbwMH8T3qxRQA\n0RqG3Y5xjNMNrC1ws5iQzKMCTHzAfWpaKAGhAB0qKext7l1aWFJGX7pYZI+lT0UAIABUM1lBcqFl\nhSVQ24BxkZ9f1NT0UAN2L6Uya2iuI3jljWSN/vKwyDUtFADFhREVFQKi42qBgCnbRu3Y56ZpaKAC\nkZQwwRmlooAiS1hj+5Gq5O7gY59akxilooARVC5wMZpaKKAIFsoFLkRKC7bmwOp9f0p8VvFDny40\nTPXaMZqSigBkcKRKoVcBeB7U+iigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACvG/j\nv4a+Gvj86P4Z8c3dlaarcP5ukPc3UdvdeYDnNu7/AMfy9ACa9krg/ib8GfB3xg0y1tvF+if2uts2\n6Fo7mW2mjOeqyROjL+BoA8GhvPEv7PnxY8FeGYPGl1488P8AiW9XS/7E1u6WbUdOzG0gn3Aj9yvl\nlP8AVgfvE+b1yfgX+zv4F+Ivjj41+I/FOiW2vX0vjXUrADUIwywRhY8eUCMqTvOeTnA9K91+H37O\nPw8+FuvNrHh3QZYNS8nyvteoand38iISpIU3Esm05VeRzgda7Tw54S0vwt/aw020S2fVr+XUrrLM\nfMuHC735JxnavAwPagD4da/uof2MfBVhPcSWHhWfxLqGnazexxkeTYLqN55Yz0A8xIUyeMGu6+K/\nw4+Hnwi8UfBzUvh3pGlaP4mvfENjZxQ6YUMlzYSSR+cxC8sgHl5cfKNwz1FfS9h8NfDNp4Kk8JQ6\nPD/wjzmZ3spSzqXklaV+WJPLuzdeCeMYrlvAf7M/w4+GGrR654e8PS2+owxFYZL/AFS7vmhBxwgn\nlkCdB93HQegoA8L8JfBDwv8AEv8Aa/8AifrHinSrfXBYiKG2tLtA0cT+VGS4z67yK4rx94A8R+P/\nANqzxFolpp/ha5tPD2mWcGhaF4nt/NRITDH5j2ymVMhWVASuQNwB6ivuDR/A2j6Drep6xY2S2+pa\nm4e4uFdmL4UDkMSP4R0Fc18R/gJ4J+LtzbzeKdIkvLq2BEd9Z39xYzgcZUyW8kbEcDgnHAoA8z/Y\nk8J3Pg7wl4s0/wDt/R9Us4temEVlom0W2nnyYcwIBI+0Dg4z/FX0fbBRu2ABSc+59f1rn/Afw+0L\n4daNFpfh6wj07TY+UiRmck4xuZ2JZ24HzMSeBzXSDAfAGOKAH0UUUAFFFFABRRRQAjZ2nHWo2IiX\ncakZgqknpXjH7TvxA1jwR8L2h8PZg8S+Ir2LQdImYBhb3VzlIpSDkEKxBOQfoaAO5m+KXg+DxIPD\nz+K9Dg8QMcDSX1GEXbHGf9Vu3dBnp0ret9XsG1I6d9vt21IIZGs/PUyqvGTtznHI5x3FfLvxK/Zi\n8P8AgD9n/U7/AEmzV/GGlxw6s2u3V3K9w00U8cspLsx4KIy7emDjHNXf2KLvVfi5BrXxo8QQG3vP\nEkUFtY2xbHkwwqUdwoO0CUhH/wAOlAH1NRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAF\nFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFNkGUPOPenVHcELA5LBABkseg+tAHEeLPjR4B8CavFpXi\nHxloWi6vMuY7S/1KGGZuB0VmBPUdquWPxT8Hav4ml8Oad4q0TU9ejH73S7fU4XuEHOd0YYsOh7dq\n+DP2/ND8A+Efgf4m1W2vY9e8XeJdb+yxajJIJJon2z/u4uf3aR7dmQATtUnPWvoT4Lfs1/CX4UfF\nGyk01nvviVpOkJFcXk95cPJJE5lXzpBv8slv3g5GRt7cUAfTMSBDgdMce3tmpa4XwN8YfCXxB1nW\nNH8P65HqupaRIYr63WJ0aBwR8pLKAeo6E9a7HDJtIZm4wAcYU+9AFmikHTnrS0AFFFFABRRRQAUU\nUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRR\nQAUUUUAFFFFABRRRQAUUUUAFFFFABTFRgSWYHPoMU+igCIwkNuVtp+nUUeQBGqqcFcYJGalooAjM\nRbq3Q5HHSkWAAAn7+BlgME1LRQAwp6HHr70GIEY+6voOKfRQA3bgYBwPQClC49zS0UAFFFFABRRR\nQAUUUUAMlG6MgKH/ANknFeP/ALRvw31zx94d0e68NNE3iDw7rFtrllBcviO4eFt/lE/wglVGcHGe\nhr2JhkEVGyE4xgMPuk+lAHy34q8H/Fj9o4waB400a1+GngpR/wATSOw1Y30upYBKpny4di79hP3u\nAR3rtP2Z/Bvir4TWuo+AtT02FvDGlzStourJd7nktmkJihMWz5fLQqud5zjoOle2IEYfKDsHcjp+\nBp8X3sZJCjqR1zQBNRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFJmjNAC0UUmR60AL\nRSZHrS0AFFJmloAKKQEHoc0ZAoAWiiigAqC+s49Rsp7WYEwzo0bgHGVIwanooA+Vb7/gmt8GtRsN\nbt57LU5ZNTupLzz5bve9pI7szGAlf3Yy56e1eneBfhD4T/Z+0PxJrcdzfaveSQPd6nrGt3BurydI\nkL7Wmb5ii/MQpJALMe5r1vI9a5P4oeEf+E/+H/iTwu95Pp8Ws6fcWLXcGN8ayxshxkHs3pQB+bP7\nL/xa+I/j7xd8TYPhPp+mJ4m1LWX1S71LW23pHaxMIEiXK/xJ5T7s8Yxg9a/TvQP7QXR7I6mUfUjC\nguWt/wDVmXHzEDsM18rp/wAE/dF0rVtNn8P+KNY0Oz/spNI1iKzeMHUIw8cuWLRkj5oo+VwePrX1\ndp2nxaPZQWluHSGCJY44c5ACjAGT/U0AaI6UtIDxzxS0AFFJkUZxQAtFFJmgBaKKKACikzRmgBaK\nKSgBaKTOaMgUALRSZzQTigBaKTOaWgAopKWgAopKMj1oAWikzmloAKKQHNLQAUUUmRnGaAFooooA\nKKTOKWgAopMj1oyPWgBaKQsB1IFFAC0UUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRR\nQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFNb5u\nKKKAGbGQHBz7GljYnqoH0NFFADs7mIpDtjPvRRQApQHnFRLKpbaA1FFAEoUA8dadRRQBGcKcDC/h\nQyY+ZiWx6UUUANSQSj5crinZP979KKKAHryOuaCdozRRQAz5iclVx655oLK3UGiigBol52qDx608\nMGHIoooAjSRWOAG/E1MMDpRRQBGzNuGFXHrmlMRJyWzRRQAM6k45J/SkBGQuCCfyoooAkAxULXCi\nUrhsj3oooAkBB5/nTJHVOob8DRRQBKpyoNMchCM5yfSiigBu9VHII+lPADqCRRRQAgyGwoG3uaJA\nAp3EkelFFACI6kbQCKkUbRjrRRQAhGDmkClSSWyPSiigBQQwyelJhVz70UUANz5eccihSJhu+Ye2\naKKAHRlTkKMYNOPSiigBuG9setMd0Q5IJPqKKKAHp82CM/iacRmiigCLcrEqASQcc07cAQBnmiig\nBWRRyRTY2YnlFH0NFFACTBCRuUsfaiiigD//2Q==\n",
       "metadata": {
        "jpeg": {
         "width": 500
        }
       },
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "<IPython.core.display.Image at 0x7554ef0>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The following is a classic estimation problem called the \"lighthouse problem\". The figure shows a set of receivers distributed at coordinates $x_k$ along the shore and a lighthouse located at some position $(\\alpha,\\beta)$ offshore. The idea is that the coastline is equipped with a continuous strip of photodetectors. The lighthouse flashes the shore $N$ times at some random angle $\\theta_k$. The strip of  photodetectors registers the $k^{th}$ flash position $x_k$, but the the angle $\\theta_k$ of the flash is unknown. Furthermore, the lighthouse beam is laser-like so there is no smearing along the strip of photodetectors. In other words, the lighthouse is actually more of a disco-ball in a dark nightclub.\n",
      "\n",
      "The problem is how to estimate $ \\alpha  $ given we already have $\\beta$.\n",
      "\n",
      "From basic trigonometry, we have the following:\n",
      "\n",
      "$$ \\beta \\tan(\\theta_k) = x_k - \\alpha $$\n",
      "\n",
      "The density function for the angle is assumed to be the following:\n",
      "\n",
      "$$ f_{\\alpha}(\\theta_k) = \\frac{1}{\\pi} $$\n",
      "\n",
      "This means that the density of the angle is uniformly distributed between $ \\pm \\pi/2 $. Now, what we really want is the density function for $x_k$ which will tell us the probability that the $k^{th}$ flash will be recorded at position $ x_k $. After a transformation of variables, we obtain the following:\n",
      "\n",
      "$$ f_{\\alpha}(x_k) = \\frac{\\beta}{\\pi(\\beta ^2 +(x_k-\\alpha)^2)} $$\n",
      "\n",
      "which we plot below for some reasonable factors\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xi = linspace(-10,10,150)\n",
      "alpha = 1\n",
      "f = lambda x: 1/(pi*(1+(x-alpha)**2))\n",
      "plot(xi,f(xi))\n",
      "xlabel('$x$',fontsize=24)\n",
      "ylabel(r'$f_{\\alpha}(x)$',fontsize=24);\n",
      "vlines(alpha,0,.35,linestyles='--',lw=4.)\n",
      "grid()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAZ0AAAEdCAYAAADXb7p6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x756fc50>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As shown in figure, the peak for this distribution is when $ x_k=\\alpha $. Because there is no coherent processing, the recording of a signal at one position does not influence what we can infer about the position of another measurement. Thus, we can justify assuming independence between the individual $x_k$ measurements. The encouraging thing about this distribution is that it is centered at the variable we are trying to estimate, namely $\\alpha$.\n",
      "\n",
      "The temptation here is to just average out the $x_k$ measurements because of this tendency of the distribution around $\\alpha$. Later, we will see why this is a bad idea."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Using Maximum  Likelihood Estimation"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Given $N$ measurements, we form the likelihood as the following:\n",
      "\n",
      "$$ L(\\alpha) = \\prod_{k=1}^N f_{\\alpha}(x_k)$$\n",
      "\n",
      "And this is the function we want to maximize for our maximum likelihood estimator. Let's process the logarithm of this to  make the product easy to work with as this does not influence the position of the maximum $ \\alpha $. Then,\n",
      "\n",
      "$$\\mathcal{L}(\\alpha)=\\sum_{k=1}^N \\ln f_{\\alpha}(x_k) = \\texttt{constant}- \\sum_{k=1}^N \\ln (\\beta ^2 +(x_k-\\alpha)^2) $$\n",
      "\n",
      "Taking the first derivative gives us the equation would have to solve in order to compute the estimator for $ \\alpha $,\n",
      "\n",
      "$$ \\frac{d \\mathcal{L}}{d \\alpha} = 2 \\sum_{k=1}^N \\frac{x_k-\\alpha}{\\beta^2+(x_k-\\alpha)^2}=0$$\n",
      "\n",
      "Unfortunately, there is no easy way to solve for the optimal $ \\alpha $ for this equation. However, we are not defenseless at this point because Python has all the tools we need to overcome this. Let's start by getting a quick look at the histogram of the $x_k$ measurements."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "beta  =alpha = 1\n",
      "theta_samples=((2*np.random.rand(250)-1)*pi/2)\n",
      "x_samples = alpha+beta*np.tan(theta_samples)\n",
      "hist(x_samples);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAEACAYAAAC08h1NAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\naozBL0mN+X9ThFBkq/ZbdAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x756f610>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The  histogram  above shows that although many of the measurements are in one bin, even for relatively few samples, we still observe measurements that are very for displaced from the main group. This is because we initially assumed that the $\\theta_k$ angle could be anywhere between $[-\\pi/2,\\pi/2]$, which is basically expressing our ignorance of the length of the coastline.\n",
      "\n",
      "With that in mind, let's turn to the maximum likelihood estimation. We will need some tools from `sympy`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import sympy as S\n",
      "a=S.symbols('alpha',real=True)\n",
      "x = S.symbols('x',real=True)\n",
      "# form derivative of the log-likelihood\n",
      "dL=sum((xk-a)/(1+(xk-a)**2)  for xk in x_samples)\n",
      "S.plot(dL,(a,-15,15),xlabel=r'$\\alpha$',ylabel=r'$dL(\\alpha)/d\\alpha$')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAWwAAAEICAYAAAB7+s71AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x94bd970>"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "<sympy.plotting.plot.Plot at 0x94adb90>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The above figure shows that the zero-crossing of the derivative of the log-likelihood crosses where the $\\alpha$ is to be estimated. Thus, our next task is to solve for the zero-crossing, which will then reveal the maximum likelihood estimate of $\\alpha$ given the set of measurements $\\lbrace x_k \\rbrace$.\n",
      "\n",
      "\n",
      "There are tools in `scipy.optimize` that can help us compute the zero-crossing as demonstrated in the cell below."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy import optimize\n",
      "from scipy.optimize import fmin_l_bfgs_b\n",
      "\n",
      "# convert sympy function to numpy version with lambdify\n",
      "alpha_x  = fmin_l_bfgs_b(S.lambdify(a,(dL)**2),0,bounds=[(-3,3)],approx_grad=True)\n",
      "\n",
      "print alpha_x"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(array([ 0.99435905]), array([  3.76209349e-14]), {'warnflag': 2, 'task': 'ABNORMAL_TERMINATION_IN_LNSRCH', 'grad': array([  1.64970679e-05]), 'nit': 5, 'funcalls': 150})\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Comparing The Maximum likelihood Estimator to Just Plain Averaging"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Whew. That was a lot of work to compute the maximum likelihood estimation. Earlier we observed that the density function is peaked around the $\\alpha$ we are trying to estimate. Why not just take the average of the $\\lbrace x_k \\rbrace$ and use that to estimate $\\alpha$?\n",
      "\n",
      "Let's try computing the average in the cell below."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print 'alpha using average =',x_samples.mean()\n",
      "print 'maximum likelihood estimate = ', alpha_x[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "alpha using average = -14.7935661293\n",
        "maximum likelihood estimate =  [ 0.99435905]\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If you run this notebook a few times, you will see that estimate using the average has enormous variance. This is a consequence of the fact that we can have very large absolute values for $\\lbrace x_k \\rbrace$ corresponding to values of $\\theta_k$ near the edges of the $[-\\pi/2,\\pi/2]$ interval."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def run_trials(n=100):\n",
      "    o=[]\n",
      "    for i in range(100):\n",
      "        theta_samples=((2*np.random.rand(250)-1)*pi/2)\n",
      "        x_samples = alpha+beta*np.tan(theta_samples)\n",
      "        o.append(x_samples)\n",
      "    return np.array(o)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "o= run_trials()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The following figure shows the histogram of the measurements. As shown, there are many measurements away from the central part. This is the cause of our widely varying average. What if we just trimmed away the excess outliers? Would that leave us with an easier to implement procedure for estimating $\\alpha$?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "hist(o[np.where(abs(o)<200)]);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYgAAAEACAYAAACpoOGTAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAEwlJREFUeJzt3X+M3PWd3/HnK3FAHEFBViKHH05MdY6CIyQ463CkpM1K\n6KjTSkB0d8FUjWhjRddwB1FOuh7mpLJppVO4KpeAKvgnzmFo4wYddwR6QDARq6Z/wCpXCE6Mi93G\nETbYqUguuSjXxm7e/WM+C3Obz3rXu+OdMXk+pJE/8/7+2Pd85zv72u/3O+NJVSFJ0nxvGncDkqTJ\nZEBIkroMCElSlwEhSeoyICRJXQaEJKnrpAGRZH2Sp5J8J8m3k9zS6tNJDid5tt0+PLTMjiQHkuxP\ncvVQfXOSvW3anUP1s5N8pdWfTvLu0/FAJUmnZrEjiOPAp6vqfcD7gd9NcilQwJ9W1RXt9hhAkk3A\n9cAmYCtwd5K0dd0DbK+qjcDGJFtbfTvwaqt/HrhjhI9PkrRMJw2IqjpaVc+18U+AF4CL2uR0FrkW\n2F1Vx6vqEHAQ2JLkAuC8qppt890HXNfG1wC72vhB4KplPhZJ0ggt+RpEkg3AFcDTrXRzkm8l2Znk\n/Fa7EDg8tNhhBoEyv36E14PmIuAlgKo6AfwoydpTexiSpFFbUkAkeSvw58Cn2pHEPcAlwOXAK8Dn\nTluHkqSxWLPYDEnewuDUz3+sqocAqur7Q9O/CDzS7h4B1g8tfjGDI4cjbTy/PrfMu4CXk6wB3lZV\nP+j04X8aJUmnqKp6lwOWZLF3MQXYCeyrqi8M1S8Ymu0jwN42fhjYluSsJJcAG4HZqjoK/DjJlrbO\njwFfHVrmxjb+LeDrC/VTVRN9u/3228feg33ap33a59xtpRY7gvgA8M+B55M822q3ATckuZzBu5m+\nC/xO+wW+L8kDwD7gBHBTvd7lTcC9wDnAo1X1eKvvBO5PcgB4Fdi24kclSVqxkwZEVf03+kcZj51k\nmT8G/rhT/2vgsk79/wIfXbRTSdKq8pPUIzQ1NTXuFpbEPkfLPkfLPidHRnGeajUkqTOlV0maBEmo\n03WRWpL0y8uAkCR1GRCSpC4DQpLUZUBIkroMCElSlwEhSeoyICRJXQaEJKnLgJAkdRkQkqQuA0KS\n1GVASJK6DAhJUpcBIUnqMiAkSV0GhCSpy4CQJHWtGXcD0pkqWfY3OY6UX8Wr08WAkFZk3L+cJyOk\n9MbkKSZJUpcBIUnqMiAkSV0GhCSpy4CQJHUZEJKkLgNCktRlQEiSugwISVKXASFJ6jIgJEldBoQk\nqcuAkCR1GRCSpK6TBkSS9UmeSvKdJN9Ockurr02yJ8mLSZ5Icv7QMjuSHEiyP8nVQ/XNSfa2aXcO\n1c9O8pVWfzrJu0/HA5UknZrFjiCOA5+uqvcB7wd+N8mlwK3Anqp6D/D1dp8km4DrgU3AVuDuvP6t\nKvcA26tqI7AxydZW3w682uqfB+4Y2aOTJC3bSQOiqo5W1XNt/BPgBeAi4BpgV5ttF3BdG18L7K6q\n41V1CDgIbElyAXBeVc22+e4bWmZ4XQ8CV630QUmSVm7J1yCSbACuAJ4B1lXVsTbpGLCujS8EDg8t\ndphBoMyvH2l12r8vAVTVCeBHSdaeyoOQJI3ekr5yNMlbGfx1/6mq+tvh7+KtqkqyKt+7OD09/dp4\namqKqamp1fixknRGmJmZYWZmZmTry2JfeJ7kLcB/AR6rqi+02n5gqqqOttNHT1XVe5PcClBVn23z\nPQ7cDnyvzXNpq98A/KOq+mSbZ7qqnk6yBnilqt7R6aP8cnZNksEfSuPeJ4OvCy0kCVW17C8uX+xd\nTAF2AvvmwqF5GLixjW8EHhqqb0tyVpJLgI3AbFUdBX6cZEtb58eAr3bW9VsMLnpLksbspEcQST4I\n/FfgeV7/U2kHMAs8ALwLOAR8tKr+pi1zG/Bx4ASDU1Jfa/XNwL3AOcCjVTX3ltmzgfsZXN94FdjW\nLnDP78UjCE0UjyA06VZ6BLHoKaZJYUBo0hgQmnSn9RSTJOmXlwEhSeoyICRJXQaEJKnLgJAkdRkQ\nkqQuA0KS1GVASJK6DAhJUpcBIUnqMiAkSV0GhCSpy4CQJHUZEJKkLgNCktRlQEiSugwISVKXASFJ\n6jIgJEldBoQkqcuAkCR1GRCSpC4DQpLUZUBIkroMCElSlwEhSeoyICRJXQaEJKnLgJAkdRkQkqQu\nA0KS1GVASJK6DAhJUpcBIUnqMiAkSV2LBkSSLyU5lmTvUG06yeEkz7bbh4em7UhyIMn+JFcP1Tcn\n2dum3TlUPzvJV1r96STvHuUDlCQtz1KOIP4M2DqvVsCfVtUV7fYYQJJNwPXAprbM3UnSlrkH2F5V\nG4GNSebWuR14tdU/D9yxokckSRqJRQOiqr4B/LAzKZ3atcDuqjpeVYeAg8CWJBcA51XVbJvvPuC6\nNr4G2NXGDwJXLb19SdLpspJrEDcn+VaSnUnOb7ULgcND8xwGLurUj7Q67d+XAKrqBPCjJGtX0Jck\naQSWGxD3AJcAlwOvAJ8bWUeSpImwZjkLVdX358ZJvgg80u4eAdYPzXoxgyOHI208vz63zLuAl5Os\nAd5WVT/o/dzp6enXxlNTU0xNTS2nfUl6Q5qZmWFmZmZk60tVLT5TsgF4pKoua/cvqKpX2vjTwK9X\n1T9rF6m/DFzJ4NTRk8CvVlUleQa4BZgF/gq4q6oeT3ITcFlVfTLJNuC6qtrW6aGW0qu0Wgbvvxj3\nPhl8XWghSaiq3vXiJVn0CCLJbuBDwNuTvATcDkwluZzBq+O7wO8AVNW+JA8A+4ATwE1Dv9VvAu4F\nzgEerarHW30ncH+SA8CrwC+EgyRp9S3pCGISeAShSeMRhCbdSo8g/CS1JKnLgJAkdRkQkqQuA0KS\n1GVASJK6DAhJUpcBIUnqMiAkSV0GhCSpy4CQJHUZEJKkLgNCktRlQEiSugwISVKXASFJ6jIgJEld\nBoQkqcuAkCR1GRCSpC4DQpLUZUBIkroMCElSlwEhSeoyICRJXQaEJKnLgJAkdRkQkqQuA0KS1GVA\nSJK6DAhJUpcBIUnqMiAkSV0GhCSpy4CQJHUZEJKkLgNCktS1aEAk+VKSY0n2DtXWJtmT5MUkTyQ5\nf2jajiQHkuxPcvVQfXOSvW3anUP1s5N8pdWfTvLuUT5ASdLyLOUI4s+ArfNqtwJ7quo9wNfbfZJs\nAq4HNrVl7k6Stsw9wPaq2ghsTDK3zu3Aq63+eeCOFTweSdKILBoQVfUN4IfzytcAu9p4F3BdG18L\n7K6q41V1CDgIbElyAXBeVc22+e4bWmZ4XQ8CVy3jcUiSRmy51yDWVdWxNj4GrGvjC4HDQ/MdBi7q\n1I+0Ou3flwCq6gTwoyRrl9mXJGlEVnyRuqoKqBH0IkmaIGuWudyxJO+sqqPt9NH3W/0IsH5ovosZ\nHDkcaeP59bll3gW8nGQN8Laq+kHvh05PT782npqaYmpqapntS9Ibz8zMDDMzMyNbXwYHAIvMlGwA\nHqmqy9r9P2FwYfmOJLcC51fVre0i9ZeBKxmcOnoS+NWqqiTPALcAs8BfAXdV1eNJbgIuq6pPJtkG\nXFdV2zo91FJ6lVbL4P0X494ng68LLSQJVZXF51xg+cV2riS7gQ8Bb2dwveHfAF8FHmDwl/8h4KNV\n9Tdt/tuAjwMngE9V1ddafTNwL3AO8GhV3dLqZwP3A1cArwLb2gXu+X0YEJooBoQm3WkPiElhQGjS\nGBCadCsNCD9JLUnqMiAkSV0GhCSpy4CQJHUZEJKkLgNCktRlQEiSugwISVKXASFJ6jIgJEldBoQk\nqcuAkCR1GRCSpC4DQpLUZUBIkroMCElSlwEhSeoyICRJXQaEJKnLgJAkdRkQkqQuA0KS1GVASJK6\nDAhJUpcBIUnqMiAkSV0GhCSpy4CQJHUZEJKkLgNCktRlQEiSugwISVKXASFJ6jIgJEldBoQkqcuA\nkCR1rSggkhxK8nySZ5PMttraJHuSvJjkiSTnD82/I8mBJPuTXD1U35xkb5t250p6kiSNxkqPIAqY\nqqorqurKVrsV2FNV7wG+3u6TZBNwPbAJ2ArcnSRtmXuA7VW1EdiYZOsK+5IkrdAoTjFl3v1rgF1t\nvAu4ro2vBXZX1fGqOgQcBLYkuQA4r6pm23z3DS0jSRqTURxBPJnkm0k+0WrrqupYGx8D1rXxhcDh\noWUPAxd16kdaXZI0RmtWuPwHquqVJO8A9iTZPzyxqipJrfBnvGZ6evq18dTUFFNTU6NatSSd8WZm\nZpiZmRnZ+lI1mt/fSW4HfgJ8gsF1iaPt9NFTVfXeJLcCVNVn2/yPA7cD32vzXNrqNwAfqqp/NW/9\nNapepVEYXEIb9z4ZfF1oIUmoqvmXAZZs2aeYkvxKkvPa+FzgamAv8DBwY5vtRuChNn4Y2JbkrCSX\nABuB2ao6Cvw4yZZ20fpjQ8tIksZkJaeY1gF/2d6ItAb4T1X1RJJvAg8k2Q4cAj4KUFX7kjwA7ANO\nADcNHRLcBNwLnAM8WlWPr6AvSdIIjOwU0+nmKSZNGk8xadKN7RSTJOmNzYCQJHUZEJKkLgNCktRl\nQEiSugwISVKXASFJ6jIgJEldBoQkqcuAkCR1GRCSpC4DQpLUZUBIkroMCElSlwEhSeoyICRJXQaE\nJKnLgJAkdRkQkqQuA0KS1LVm3A1Iy5Us+7vYJS2BAaEzXI3xZxtQemPzFJMkqcuAkCR1GRCSpC4D\nQpLUZUBIkroMCElSlwEhSeoyICRJXQaEJKnLgJAkdRkQkqQuA0KS1GVASJK6JiYgkmxNsj/JgSR/\nOO5+JOmX3UQERJI3A/8B2ApsAm5Icul4uzp1MzMz425hSexz1GbG3cCSnCnb0z4nx0QEBHAlcLCq\nDlXVceA/A9eOuadTdqbsMPY5ajPjbmBJzpTtaZ+TY1IC4iLgpaH7h1tNkjQmk/KNckv6WrCf/vSn\nnHvuuae7l0Xddddd3HzzzWPtYaVft/mZz3xmRJ2cXmdKn+N0KvvCmbI9T7XPqnF+s+AbVyZhwyZ5\nPzBdVVvb/R3Az6vqjqF5xt+oJJ1hqmrZf01OSkCsAf4HcBXwMjAL3FBVL4y1MUn6JTYRp5iq6kSS\n3wO+BrwZ2Gk4SNJ4TcQRhCRp8kzKu5hek+TfJ3khybeS/EWStw1N29E+SLc/ydVD9c1J9rZpd65S\nn7+d5DtJ/l+SXxuqb0jyd0mebbe7x9XnQj22aROzLef1NZ3k8ND2+/BiPY/LJH+4M8mhJM+3bTjb\namuT7EnyYpInkpw/hr6+lORYkr1DtQX7GtdzvkCfE7dvJlmf5Kn2Ov92kltafTTbtKom6gb8BvCm\nNv4s8Nk23gQ8B7wF2AAc5PUjoFngyjZ+FNi6Cn2+F3gP8BTwa0P1DcDeBZZZ1T5P0uNEbct5Pd8O\n/H6n3uv5TWPcT9/cetjQenoOuHRc/XT6+y6wdl7tT4B/3cZ/OPfaWuW+/iFwxfBrZKG+xvmcL9Dn\nxO2bwDuBy9v4rQyu5V46qm06cUcQVbWnqn7e7j4DXNzG1wK7q+p4VR1i8MC2JLkAOK+qZtt89wHX\nrUKf+6vqxaXOP44+T9LjRG3Ljt67Lno9X7mqXf19Z8KHO+dvx2uAXW28izE8t1X1DeCH88oL9TW2\n53yBPmHC9s2qOlpVz7XxT4AXGHyGbCTbdOICYp6PM/grFuBCBh+gmzP3Ybr59SOM/0N2l7RD0Jkk\nH2y1i5icPid9W97cTjHuHDo0XqjncZn0D3cW8GSSbyb5RKutq6pjbXwMWDee1n7BQn1N2nMOE7xv\nJtnA4KjnGUa0TcfyLqYkexgcGs13W1U90ub5I+BnVfXlVW1uyFL67HgZWF9VP2zn/R9K8r4J63Gs\nTtLzHwH3AP+23f93wOeA7QusapzvsJj0d3d8oKpeSfIOYE+S/cMTq6om8bNFS+hrnD1P7L6Z5K3A\ng8CnqupvM/ThyZVs07EERFX9xsmmJ/kXwD9h8LmIOUeA9UP3L2aQfkd4/TTUXP3IavS5wDI/A37W\nxv89yf8ENp6uPpfTI2PYlsOW2nOSLwJzIdfreeS9nYL5/azn7/9lNlZV9Ur7938n+UsGpxGOJXln\nVR1tpxO/P9YmX7dQXxP1nFfVa9trkvbNJG9hEA73V9VDrTySbTpxp5iSbAX+ALi2qv7P0KSHgW1J\nzkpyCYNfurNVdRT4cZItGcTmx4CHfmHFp7nt1wbJ2zP432lJ8g9an/+rvWDH2efwudOJ3ZZtZ57z\nEWDuXSTdnlezt3m+CWzM4F1rZwHXtx7HLsmvJDmvjc8FrmawHR8Gbmyz3cjqv04WslBfE/WcT+K+\n2V6nO4F9VfWFoUmj2aarcaX9FK/KHwC+BzzbbncPTbuNwUWV/cA/HqpvZvBkHQTuWqU+P8LgHPTf\nAUeBx1r9N4Fvt97/Gvin4+pzoR4nbVvO6/k+4HngW22nXrdYz2PcVz/M4F0jB4Ed4+5nqK9LGLxT\n5bm2L+5o9bXAk8CLwBPA+WPobTeD07A/a/vmvzxZX+N6zjt9fnwS903gg8DP23M99ztz66i2qR+U\nkyR1TdwpJknSZDAgJEldBoQkqcuAkCR1GRCSpC4DQpLUZUBIkroMCElS1/8H/Tb0N4AC8GwAAAAA\nSUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x778e7b0>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The following graph shows what happens when we include only a relative neighborhood around zero in our calculation of the average value. Note that the figure shows a wide spread of average values depending upon how big a neighborhood around zero we decide to keep. This is an indication that the average is not a good estimator for our problem because it is very sensitive to outliers."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot(range(100,10000,100),[o[np.where(abs(o)<i)].mean() for i in range(100,10000,100)],'-o')\n",
      "xlabel('width of neighborhood around zero')\n",
      "ylabel('value of average estimate')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "<matplotlib.text.Text at 0x9a27430>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAZQAAAEPCAYAAABlZDIgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n55wrCk8ozjnniuL/A3T9noDfVAPEAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7554c10>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For some perspective, we can wrap our maximum likelihood estimator code in one function and then examine the variance of the estimator using our set of synthetic trials data. Note that this takes a long time to run!"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def ML_estimator(x_samples):\n",
      "    dL=sum((xk-a)/(1+(xk-a)**2)  for xk in x_samples)\n",
      "    a_x  = fmin_l_bfgs_b(S.lambdify(a,(dL)**2),0,bounds=[(-3,3)],approx_grad=True)\n",
      "    return a_x[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# run maximum likelihood estimator on synthetic data we generated earlier\n",
      "# Beware this may take a long time!\n",
      "v= np.hstack([ML_estimator(o[i,:]) for i in range(o.shape[0])])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "vmed= np.hstack([np.median(o[i,:]) for i in range(o.shape[0])])\n",
      "vavg =  np.hstack([np.mean(o[i,:]) for i in range(o.shape[0])])\n",
      "fig,ax = subplots()\n",
      "ax.plot(v,'-o',label='ML')\n",
      "ax.plot(vmed,'gs-',label='median')\n",
      "ax.plot(vavg,'r^-',label='mean')\n",
      "ax.axis(ymax=2,ymin=0)\n",
      "ax.legend(loc=(1,0))\n",
      "ax.set_xlabel('Trial Index')\n",
      "ax.set_ylabel('Value of Estimator')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "<matplotlib.text.Text at 0x9a2ca30>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAdUAAAEPCAYAAAAUHF6+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQRUAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x9bdc190>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The above chart shows that the using the mean-based estimator jumps all over the place while the maximum likelihood (ML) and median-based estimators are less volatile. The next chart explores the relationship between the ML and median-based estimators and checks whether one is biased compared to the other. The figure below shows that (1) there is a small numerical difference between the two estimators (2) neither is systematically different from the other (otherwise, the diagonal would not split them so evenly )."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig,ax = subplots()\n",
      "ii= np.argsort(v)\n",
      "ax.plot(v[ii],vmed[ii],'o',alpha=.3)\n",
      "axs = ax.axis()\n",
      "ax.plot(linspace(0,2,10),linspace(0,2,10))\n",
      "ax.axis(axs)\n",
      "ax.set_aspect(1)\n",
      "ax.set_xlabel('ML estimate')\n",
      "ax.set_ylabel('Median estimate')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "<matplotlib.text.Text at 0x9a45d30>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAARYAAAEPCAYAAACHlOscAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nWAzD8BwTFsMwPMeExTAMz/n/6lT0G+skdw4AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x9a2c910>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig,ax = subplots()\n",
      "ax.hist(v,10,alpha=.3,label='ML')\n",
      "ax.hist(vmed,10,alpha=.3,label='median')\n",
      "ax.legend(loc=(1,0))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "<matplotlib.legend.Legend at 0x1aa258f0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAcIAAAEACAYAAAAgOHb6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nCBpBCAAI2v8D7/l3e6uyg3kAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x9a27710>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Maximum A-Posteriori (MAP) Estimation"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's use a uniform distribution for the prior of $\\alpha$ around some bracketed interval\n",
      "\n",
      "$$ f(\\alpha) = \\frac{1}{\\alpha_{max}-\\alpha_{min}} \\quad where \\quad \\alpha_{max} \\le \\alpha \\le \\alpha_{min}$$\n",
      "\n",
      "and zero otherwise. We can compute this sample-by-sample to see how this works using this prior."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "alpha  = a\n",
      "alphamx,alphamn=3,-3\n",
      "g = f(x_samples[0])\n",
      "xi = linspace(alphamn,alphamx,100)\n",
      "mxval = S.lambdify(a,g)(xi).max()\n",
      "plot(xi,S.lambdify(a,g)(xi),x_samples[0],mxval*1.1,'o')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "[<matplotlib.lines.Line2D at 0x1aacd610>,\n",
        " <matplotlib.lines.Line2D at 0x1aacd770>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXgAAAEACAYAAAC57G0KAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n4A0x2YuoAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1aa1dbf0>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xi = linspace(alphamn,alphamx,100)\n",
      "palpha=S.Piecewise((1,abs(x)<3),(0,True))\n",
      "\n",
      "def slide_figure(n=0):\n",
      "    fig,ax=subplots()\n",
      "    palpha=S.Piecewise((1,abs(x)<3),(0,True))\n",
      "    if n==0:\n",
      "        ax.plot(xi,[S.lambdify(x,palpha)(i) for i in xi])\n",
      "        ax.plot(x_samples[0],1.1,'o',ms=10.)\n",
      "    else:\n",
      "        g = S.prod(map(f,x_samples[:n]))\n",
      "        mxval = S.lambdify(a,g)(xi).max()*1.1\n",
      "        ax.plot(xi,S.lambdify(a,g)(xi))\n",
      "        ax.plot(x_samples[:n],mxval*ones(n),'o',color='gray',alpha=0.3)\n",
      "        ax.plot(x_samples[n],mxval,'o',ms=10.)\n",
      "        ax.axis(ymax=mxval*1.1)\n",
      "    ax.set_xlabel(r'$\\alpha$',fontsize=18)\n",
      "    ax.axis(xmin=-17,xmax=17)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "interact(slide_figure, n=(0,15,1));"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAW8AAAEXCAYAAABiTcW4AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1b6296d0>"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Does the order matter?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig,axs = subplots(2,6,sharex=True)\n",
      "fig.set_size_inches((10,3))\n",
      "for n,ax in enumerate(axs.flatten()):\n",
      "    if n==0:\n",
      "        ax.plot(xi,[S.lambdify(x,palpha)(i) for i in xi])\n",
      "        ax.plot(x_samples[0],1.1,'o',ms=10.)\n",
      "    else:\n",
      "        g = S.prod(map(f,x_samples[:n]))\n",
      "        mxval = S.lambdify(a,g)(xi).max()*1.1\n",
      "        ax.plot(xi,S.lambdify(a,g)(xi))\n",
      "        ax.plot(x_samples[:n],mxval*ones(n),'o',color='gray',alpha=0.3)\n",
      "        ax.plot(x_samples[n],mxval,'o',ms=10.)\n",
      "        ax.axis(ymax=mxval*1.1)\n",
      "        ax.set_yticklabels([''])\n",
      "        ax.tick_params(labelsize=6)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAlIAAADDCAYAAABJev+8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1ae172b0>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# use random  order for first 12 samples\n",
      "x_samples[:12]= np.random.permutation(x_samples[:12])\n",
      "fig2,axs = subplots(2,6,sharex=True)\n",
      "fig2.set_size_inches((10,3))\n",
      "\n",
      "for n,ax in enumerate(axs.flatten()):\n",
      "    if n==0:\n",
      "        ax.plot(xi,[S.lambdify(x,palpha)(i) for i in xi])\n",
      "        ax.plot(x_samples[0],1.1,'o',ms=10.)\n",
      "    else:\n",
      "        g = S.prod(map(f,x_samples[:n]))\n",
      "        mxval = S.lambdify(a,g)(xi).max()*1.1\n",
      "        ax.plot(xi,S.lambdify(a,g)(xi))\n",
      "        ax.plot(x_samples[:n],mxval*ones(n),'o',color='gray',alpha=0.3)\n",
      "        ax.plot(x_samples[n],mxval,'o',ms=10.)\n",
      "        ax.axis(ymax=mxval*1.1)\n",
      "        ax.set_yticklabels([''])\n",
      "        ax.tick_params(labelsize=6)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAlIAAADDCAYAAABJev+8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1b629130>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAlIAAADDCAYAAABJev+8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJztnWl0VNeVqL/DjJiEBjSAQYAZPZEAJk5sQgY/3Hbb7ddx\nO3Pe69h56XjF/TL063Q7A3Yn7sRpe3Xczugk7dg9OHHI5KzEc8AjGOzYBAyyDUIIoYHSjBAgCZ33\n4+iqSlW3qq5Kd6za31osVFX31t2177nn7LP3PvsorTWCIAiCIAjC2JkQtACCIAiCIAhRRQwpQRAE\nQRCEHBFDShAEQRAEIUfEkBIEQRAEQcgRMaQEQRAEQRByRAwpQRAEQRCEHMlqSCml/l0p1aqU2pvm\n8w8rpfYopf6klHpeKXWh+2IKgiAIgiCEDyceqfuAKzJ8Xgds1FpfCHwVuNcNwQRBEARBEMJOVkNK\na/0s0Jnh8x1a6+7hly8CC1ySTRAEQRAEIdS4nSN1A/B7l79TEARBEAQhlExy64uUUu8CPg68I83n\nshfNONFaq1zPFf2PD9F9sIj+g0X0Hxyi+2Bxon9XPFLDCeY/BK7RWmcKA+b8b8uWLQV9vhsEJX/Q\nuitk3efD+aJ/0X9UdVfIus+H850ybo+UUmoh8EvgI1rrg+P9vjDT19fHM88/w9bHttLQ3sDC0oVc\nt/k6Nr5jI0VFRUGLV3DI/fCORN1ue3Ibjb2NolsXKbS2e+Pf3ZjXv09wF+v5ePjxh3nhyAuhfz6y\nGlJKqQeBdwJlSqmjwBZgMoDW+gfAV4C5wPeUUgADWuuLPZM4IH7+u59z/977OTbnGANVA1AD9MMD\nDz7A/O/PZ33Feh767kNBi1kwXH/T9exu3S33wwNSdFsMdVPrRLcuUYht98dTf5zXv09wj1HPx8Ro\nPB9ZDSmt9QezfH4jcKNrEqVh06ZNgZ3f19dH+/R2Wi9sHf3BFBhYNEA99bDHHJfOWh6v/EEzHvnd\nvHexWIz9+/fzXMNzNK9vHn1gmvsRBt3feuutI39v2rRpTDL52fb7+vrY3bqb+gvr42/WMEq3Z3ad\n4emnn2b16tUA1NXVjRy6ZMkSysvLc74+wPbt29m+ffuYzvESN/Vvq1+wbbsnT56krq6OefPm8eKL\nLzJ79mx6enpGTlmyZAngvv49YQx9ZTJe9T2xWCyj7mKx2IjugRT9292PMOrekt9Ovmx41fek033K\n8zE0fEBS/3PkyBGKiopC0/aVW3HYrBdSSvt1Lbd59IlHuebBaxhYNJD2mMn1k3n4Qw9zxeWZSm7l\njlIKPc6kw6jq38Iyot449AY3PXsTgzWDaY91834Uku6dtPVJhyfx3Y3fZV7pPJRSrFixYuSzlpYW\nVq9ePeYOOxP5pH+nfckDVz5A1bwqKisrAejp6eGll15izZo1lJSUAFBbWxsZ/XNr/LXXfaUTrL7E\n0i+M1l3y58n67+jo4NVXX2XdunXMnj075Xy3cEP3tbW1nsmXC5l0//KrLzvqf25Zcgtr16wNTduX\nLWIcsPWxrcYFn4GB6gG2PrbVJ4kKk7q6OiorK3lsx2MMVqc3okDuR644aeuD8wfNPRgcZMKE0V1I\nZWUl9fX1HkoYbZz2Jf/92/9OGWhWrFhBU1PTyHuR0v+2+L+BgeCfTasvSSRRd8mfJ+u/qamJFStW\n0Nraant+rmzfvp1bb7115J+bhKVtZNK90/7nuT3Phartu1b+IJ9paG8w4Y1MTIGGpgY/xMmZ8YSX\nwkRzd3P2sq/juB9hCy35idO23tzdnHZly9DQkM1JAjjXb2tvq+1HifqOlP7fNfplQ304+8psurP0\nnfy/0/Ozkdwv33bbbeP6vmRC2TaGGRoacvx8tJ1qC1XbF0PKAQtLF0I/MCXDQf3Dx4UYt2c4QVE1\np8rT++F1ZxZmnLb1qjlVKKUYXmAyiuSZohDHqX4rZlbYfpSo78jqP8R9ZTbdWfpO/t/p+UETZvkm\nTJjg+Pkom14WqrY/7k2Lh4/5N6XUm8ObF7/FXRGD57rN1zG5eXLGYyY3Tea6zdf5JFFhsmTJElpa\nWth8yWYmNWWeA8j9yA0nbX3SsUnmHkyalDIDbGlpoaamxkMJo43TvuRDV3+IlpaWkfcqKyt5/fXX\nqa6uHnkvqvoPw7Np9SWJJOou+fNk/VdXV/P6669TUVFhe34YCYt8mXTvtP+59KJLQ9X2syabK6Uu\nA3qBB7TWF9h8fiXwaa31lUqpDcDdWuu32RwXmoTPsdLX18d5Hz0vdaVNAjV7anjtP1/zrMZFPiXc\njodYLEZtbS3vv+P9qav2EnDzfhSS7p209apdVfzsH37GypUrAaivr2doaIgJEyZQU1PjejJrPul/\nLH3JyZMnR+l25syZ9Pb2jtI1REP/icnmXveVTonFYhl1l/x5sv7t7kcYdX/DDTeglKK4uJirrroq\nFCkd6XTvqP/ZXcWO7+ygqKjI9bafnNZx2223OdK/k/IHzyqlajIccg1w//CxLyqlipVSFVpr+yB/\nBCkqKmJ9xXrYg6ltUT1gXI/9ZnY1v3s+6yvXB94xFALl5eWUl5dz6YOXsnvPbrkfLuOorS9az2WX\nXTZyTtCrgKLEWPqSoqIiR7qNhP5D+GxafUmun0eFH/3oR0GLkEI63Tp6PhauZ9GiRSPf4ya5pnU4\nKn8wbEj9No1H6rfA17XWLwy/fhL4gtb65aTjQjMrtBgagp/8BE6dcnZ8f38fB+ue4ZVDW+nsb2Du\nlIW8Zel1nLtkI1OmFLFhA6xb542s+TQrdwu/qkMXou7DVHnbDf1v2bJl5HUYFlqESb/J5DorT4dS\nSt/w+RtC8/uiRCH2PRCe58Op/t0ypL6htX5++PWTwN9rrf+YdFzoOrPmZqiuhptuGv93PfUUXHgh\nPORSwVUvOrMoPlB2XH89/OVfwgc+4M/1CrUzy0R/P1x1FbzvffA3f+PttUT/cb7xDdNv3X23f9cU\n/cPevfDhD8PWrbB8uX/XFd1DV5fpaz7/edPv+4mfhtT3ge1a658Ov64F3pkc2gvjDW1qgrVrTcc0\nXh58EH7zG/jpT8f/XXbIA2Vob4eyMti8GR591J9riu5T+fWv4VOfMn8fOwZeLpYR/ceZMwd6euD0\naZg61Z9riv7hk5+EH/4Q/vEf4fbb/buu6B6+8x3YsgWWLoXhIu2+4WdBzoeBjw1f9G1AV1Tyo7QG\nmxWUOaGU+T7BW/btg6oq2L8/aEkKm23b4LOfhenT4Y03gpamMGhrM/3MeefBa68FLU1h8dRT8M1v\nws6dQUtSeDz5JNx5p/EKnjwZtDT2OCl/8CDwArBCKXVUKfVxpdQnlVKfBNBa/x6oU0odBH4AuBAo\n8wcxpKLHoUPw7ndDa6uZlQvB8Morxpv71reavwXvqa2FlSth1Srzt+APnZ1w/LhJKRAD1n9efhku\nuwxWrAjvBHrcmxYPH/Npd8TxHzcNqbCTD5XNjxwxLt6qKhNSWrrU/WsUcmVzp9TWmgFdBnX/qKsz\n7f2cc8zfgj/s2werV8OCBSas2tsLM2cGLVVh0NNj0jkWLzaG1Ouvw/r1QUuVSkFXNnfbgxR2j1Q+\nVDY/dgwuvtgMJo2N3hhSXlQ2zwcj1uLECeNir6qCc8+FJ55w9/vFkLXnyBGoqTFt/+WXsx4uuIQ1\naZgwARYuhIYGY1gJ3vPmm6aPmTABliyBw4eDlsiegjekJLQXLZqazErLqip3Fgn4RT4YsRZHjpgB\nRSlYtMi8dpNC3qInE0ePmlDqwoUm2V/wh0OHzGAOxogVQ8o/6uqMAQWmrwnrBEIMKTGkIkVLizGi\nomZI5RONjWZAgbhnUPCexka4+mqYP994ZqNElD2yhw/Dtdeav6urve13xBs7moYGY0CBCa2GdQJR\n0IYUFFaOVD7Q2grz5pl/sVjQ0hQmllcQzP9NTe5OSgR7rLp3UTekokbiYG61d6+QtILRJE7a/Jg8\n52rIZjWklFJXAN8CJgI/0lrfkfR5GfCfQOXw992ptf7JmCUJgELLkYo6WhvjyTKkZClyMDQ3Q2Wl\n+Xv6dPOvsxNKSoKVK99pbjaDSUmJSXg+fRqmTQtaqvzn6FHjDQGoqIheon+UjdimJtiwwfzthyGV\nqyGbsfyBUmoi8G3gCmA18EGl1Kqkwz4NvKK1XgNsAu5SSkXC0yWhvWjR3W0G7alTxSMVJK2tcUMK\nzN9Jm7kLLnP2rFm9VF5uEm8rKkTnfnD2rGnvVVXmdUWFeS34Q1NTXPfl5dDRYe5J2MhWR+pi4KDW\nul5rPQD8FPiLpGOagdnDf88G2rXWg+6K6Q1iSEWLWMw8TGD+F0MqGI4fN4ashRi13tPWBnPnwuTJ\n5nVVlRhSftDaajyAlt6lrftLS0t80jZpEhQXm2chbGQzpOYDRxNeNw6/l8gPgfOUUk3AHuD/uiee\nt4ghFS3EkAoHVnjVoqxM7oXXWLmBFuIF9AdrcYtFebmZSAj+0NpqvIAWYe33s4XgnJgGtwCvaq03\nKaWWAk8opS7SWp9IPjCMSW9hTTaX1RuptLWZQRvM/2GcmRQCifcBwtu55RPHj48eUCorJcTkB4ke\nETBtXfodfzh9Gs6cMftLWoTVI5jNkDoGnJPw+hyMVyqRtwO3A2itDymlDgMrgJeSvyxsSW9hTjaX\n1RuptLXFPVJz5piikAMDcbe7W4gRm5m2Nigtjb8uKzP5O4J3HD8eb/sgOVJ+kWzAlpaati6rVL0n\nFjN9S6Kew+r9zmZIvQQsU0rVAE3A+4HkLWNqgfcCzyulKjBGVCTWNRRaaC9shuxYSRzAJ0wwuQvt\n7aNnjG4gBSHTo7XRebIh5XZRTreJ+iQieUCvqPBu3zGZSMRJzgecMgWKiqCry+SsCd6RnEIA4Z20\nZTSktNaDSqlPA49hyh/8WGt9IGHD4h8A/wzcp5Tag8m5+nutdYfHcrtCoRlSUSc5pGSF99w2pIT0\n9PWZtl5UFH+vpCT8GxdHfRKR7JGqrIQ//MGba8lEIk6yAQvxwVwMKW9J7u8huh4ptNaPAI8kvfeD\nhL/bgKvdF80fwpojJaQSi8Hy5fHXkpvjPx0do71RYF53RGLqFF1isdGbtcoyfH+IxeD880e/V1pq\nBnlr2xjBG+wMqdJSqK8PRJyMZFu1l9eEOUdKSCUxRwri+QqCf3R0pBbenDtX7oPXJK5YBTGk/CK5\nz4HwhpfyjXQeqTDqPhKFM71CQnvRwi60Jx4pf+nsTA1plJSY9wXvEEMqGGIxew9sGAfzdEQ1PzB5\nUQt4r3vPtojJZ8SQihZ2y+6jshQ5qp1ZMuk8Um4aUpLsnMrx46Pb/uzZMDhoVq7OmBGcXPlOe7t9\neCkq/Q5ENz+wrQ1Wrx79nrXAyCtyzQ8c9157w8dsAv4VmAy0aa03JR8TRsSQihbJs/KysujsexXV\nziyZjo5Uj9TcueZ9t54nSXZOJTnEpFTcK7VkSXByOSWqE4l0eTpeDeYyiYiTvDoYwusNzGhIJey1\n915MTandSqmHtdYHEo4pBr4DbNZaNw5vYhwZJNk8GvT3m41ai4vj75WXw4svBidTIWIX2ps61dTy\nOnkSZs4MRq58ZmDAtP1kvVtFOaNmSEWF/n7TpmfPHv1+WRns2ePNNWUSESdKhpQbe+19CPiF1roR\nRlbxRQJJNo8O1sxwQkKLlVV7/mNnSIH74T0hjrXUfkJSb11RAc3NwchUCFgrVJP1HtbBPN+wC6sW\nF5tJxWDIdvPNFtqz22tvQ9Ixy4DJSqltwCzgbq31f7gnoncUWmgvqu51sC/O5pUhJe719HR2woIF\nqe//5V/6L0uhkBzStpBtYrzFziMC0cuRiip2+p8wwRhTHR2p40GQuLHX3mTgrcB7gCJgh1Jqp9b6\nzeQDwzaQh9mQ8mIwj6J73cJuMKmo8GYDUXGvpyedR+qee/yXpVCwy9MB2bjYa+xWjYGsFvaLTIZs\n1AwpJ3vtHcUkmJ8CTimlngEuAjIaUmEhrDlSMpiPJnkXcIiv2hsaSnW/C96QzpASvCOTIeVVro6Q\nfiAPay2jfOL0aRO+s1uRGkaPYLbhZ2SvPaXUFMxeew8nHfMb4FKl1ESlVBEm9OfRLlDuIjlS0SF5\niwwwCc6zZklVbT/p7Byd8C94T6bQnuRIeUc2Q0r6e++wdG/noAijITvuvfa01rVKqUeBPwFDwA+1\n1pExpMIa2hNG09Jiv6eetQTcbsYuuI94pPwnk0dKcqS8wy7ZGcwq1WnToLtbJhVeka7NQ3yP1TAx\n7r32hl/fCdzprmjeI4ZUdGhpgZUrU9+38kTOO89/mQoRu4Kcgre0tcHSpanvi0fKW9ra0ufhWAtd\nxJDyhrwzpPIZMaSiQ0sLVFWlvl9VJYOJXwwNmVm4eKT8JRaDDclrpYl7Y93sx4Q47e2wapX9Z5Yh\ntWyZvzLlQtgWeTkhXaI/eJvsL1vE5EhYk82F0TQ3iyEVNCdOQFERTIpgrxHFwcQi3ey8qMiEmbq6\n3DVupfyHIZNXZN686KzcC+Mir2zYbRZtUVYG+z1KHvJsi5h8RpLNo8OxY1Bdnfp+VZX5TPCeKIf1\nojiYWGQaVKzQtpuGlKwYNmQzpCQ/zTtisfS6D+MeqwW9aFxCe9Hg9GlTzdbO1Tt/PjQ1+S9TIWJV\n2Bb8JdOgIh5Z78hkwEbJIxVF7AowW8yb5039wPHgyqbFw8etB3YA12utf+mqlB5RaIZUVMMbljfK\nrlbUggXQmFzZbJx4XQw1SrpPxNoyw2sktBRH68yeESnK6R2ZDNiKCjh40F95Conjx2HjRvvPImdI\nOdm0OOG4O4BHgUhlCxVSjlRUwxtHj8I559h/tmCB+dxNvAhtRFX3iaSrq+M2ElqK09sLEyeafCg7\nouKRitpEwtqwON2qvMpKeP55968rkwiDXQFmC8uQCtMii2weqZFNiwGUUtamxQeSjrsZ2Aqsd1tA\nL5EcqWiQyZCaP9/MyAcHo5kEHSX8MqSEOOmKcVpExSMVtYmE3SbpiXhVekImEYZMhtSMGcaA6u01\nBZnDQLYcKbtNi+cnHqCUmo8xrr43/FZkzIlCC+1Flfp6qKmx/2zKFPPAScK597S3Zx7UBffJZkhF\nxSMVNVpbM+/lFhUDNqpkMqQgfPp3Y9PibwH/oLXWSilFhtBe2Ny7YTakxMUb5/BhuOSS9J8vXmyO\nWbTIP5kKkba2aNTNySecGFJhGlDyhWwDeXW1WeQSpvBSvnDqlFlglGlhi+URDEt/5MamxWuBnxob\nijLgz5RSA1rr5D35QufeDbMhJS7eOHV18KEPpf988WI4dAhCnnYReWIxePvbg5aisMi0egmkurlX\nZDOkZs0yYb+eHpgzxz+5CoGmJtOuM43NYZtAZDOkRjYtBpowmxZ/MPEArfUS62+l1H3Ab+2MqLBS\nSMnmUeXgwcwzj3PPlRU0fnD8eOZBXXAfu826E6muFkPKC9IVAE6kutqkFIgh5S7Hjpnc10xUVYWr\n7M24Ny32QUbPkGTz8NPba5bdL1iQ/pjly+Ghh/yTqVDJNqgL7nP8eOYBvaQE+vpMOGT6dP/kynea\nm7OnCixYYAb91av9kSlXwpZSk43Gxsz9PXhXP9CzLWKcbFqc8P5fj1mCAAlzaE8wvP668ThNnJj+\nmJUrobbWP5kKlWzhDsF9WlvhoovSf65UPPF28WL/5Mp3jh3LHsb2ooadF4QtpSYbmVZpWyxYAH/6\nk/vXzjWlRiqbiyEVal57Dc47L/MxK1aYPKr+fn9kKkQGBsyebukKFAre4MR4tUJMgns48Yqcc477\nNewEOHIk/Spti7AZsQVfeaeQcqSi5uIF2LsXLrgg8zHTphk3/OuvZz/WCbJiMpXWVhPWy+QZFNzH\nqSEVpnyRfMCJV2ThQti1yx95ConDh+HKKzMfEzYjtqANqULLkYqaixfglVfgc5/LftyaNeZYNwwp\nWTGZSlOT/abRgrc4SXoO2+w86vT3m1If2dr7okWSm+kFhw7BkiWZj1mwwPRJZ8+GY3InoT0J7YWW\noSF4+WVYuzb7sX/2Z9HwCkYVJ6EOwV36+52FU+fPl9CemzQ0GOM1204JNTUmDCW4x8CA0enSpZmP\nmzrVeMjD0u4deaSybVyslPow8PeYYpwngE9prT1IBXMXMaTCzeuvm6JsThKc/9f/8l6eQubo0Wgb\nUlEMa7e0mLafbca9YAHs3u3edQs9tF1Xl30gBxPaa2gIj1ckHzh40Oh16tTsx9bUmHu1cKHnYmUl\nqyHlcOPiOmCj1rp72Oi6F3ibFwK7iRhS4ebZZ+HSS4OWQgAzYIShw8qVKIa1jx1zFk51O1+k0EPb\nb7xhSqpkY/p04y1sbJRdFdxi3z44/3xnxy5ZYgypMMyJnHiksm5crLXekXD8i0Bk5q6FlGweNZ54\nAq66Kmgp3CGKHpFEsm3T4yaF7hGxaGzMnvAMZuD54he9l2c8RKn9799vSqo4YelSk9PjliFV6G3/\nlVdMvqsTzj3X6D4MODGk7DYu3pDh+BuA349HKL8otGTzKNHfD08+Cf/2b0FL4g5R9IgkcvBg9gRQ\ntyh0j4hFQ4MzQ6q4GP78z72XZzxEqf3v2wfve5+zY61dFd79bneuXeht/8UX4fOfd3bssmXwq195\nK49TnBhSjs0DpdS7gI8D77D7PGyzkjCH9gp9ZvLUU7BqVfYVS4L3DA2ZwcJJuENwj/p6Z7k6gnsM\nDcGePc69IsuXm1CgMH7OnDHlJJx6vpcvN3m0YcCJIeVk42KUUhcCPwSu0Fp32n1R2GYlYTakCn1m\n8sADmTcqFvzj8GGTCzJzZtCSFBZ1dfDe9wYtRWFRW2vaemmps+NXroQf/chbmcZL2BwY6Xj+eTN5\nnjvX2fErV8Kbb7qb7O/ZFjE42LhYKbUQ+CXwEa11pLaPlRyp8NHcDI8+Ct/9btCSCGC2YnCjPpcw\nNg4eFI+U3zzzzNgWuKxaZXKqwkzYHBjp2LoVrr3W+fEzZphVrYcOuectz9WB4WSvPScbF38FmAt8\nTxmLYkBrffEYf4PvFFqOVFRmJt/8JnzsY85nJm5T6GHVZF56yVktL8E9rHo6554btCSFxSOPwPXX\nOz9+6VJTpqK3Vzy24+HkSVPc9KWXxnbehReaiV7QaQdK+zT6K6W0X9dyypNPwte/bvJxxsuePfDR\nj3qzkSKAUgqtdc5+rzDq344DB+Cyy8wee2HZILdQdJ+OTZvgC18wRU+DoBD1byU8hyEHpFD039Vl\nVt/V149tErdunVkUk22T41woFN3feSfs3Gm8UmNhyxYYHITbb/dGLqf6l8rmIc2RKkROnYKPfAS+\n+tXwGFGFzsmTprq81PPyl7EsAxfc4b77zGRhrJ7wtWvNMyLkRksL3HGH6ffHyrp17hajzZWC32tP\nDKlwcOYMfPCDJoHwb/4maGkEi0cegQ0bYNasoCUpLHbsMHoX/KG7G/7lX+B3vxv7uX/3d84qcQup\naA2f+hR84hMm32ysXHKJmXwPDmbf0sdLCtojBZJsHgYaG+Hyy83Ki/vuE12GiR//2HRUgr889VQ4\nKjYXAlrDzTfDNdfAW94y9vOXLYt21f8g+elPzcq7LVtyO7+sDK64wni1giSrIaWUukIpVauUelMp\n9YU0x/zb8Od7lFI5NMXsjDf51+78sXiQnFw/0/dFPXl5PPKnO7ezE772NRPC2LwZfv5zmDLF3Wu7\ncX7QBPX7d+6EvXuhujqY64cFv/W/bx/09cVDe9L+t3t67t13w6uvwl13uXttN84PGi9/fywGn/0s\n/Pu/p/foObn+z36Wfh9Qv/Sf0ZBK2GfvCmA18EGl1KqkY64EztVaLwP+D/A9LwT1ypBy6v3Idv1s\nob1CfqDSnfulL5lidjt2mC0uJqRpjdKZbff9/FjMrJy86y544QX/rx8m/Nb/t74FH/94/HmQ9r/d\ns3O3bjUhvd/+1iynd/PabpwfNF79fq3hppuMt/viDOv7o6L/bFHFrPvsAdcA9wNorV9UShUrpSq0\n1q0eyOsqkiMVLN/+toTxwsbQkMmL+tu/NZ3c+98PESlDkxf8+tdG//v2BS1J/vOrX5nB/LHHZNNh\nP9Ha9Cl1dfAf/xG0NO6QzZByss+e3TELgNAbUiCGVJCIERUsO3eaJd9tbWZft9deg6efhvJy4xW5\n+uqgJcxf+vuho8PUH2prM57Z3/0OnnvOGFNB1VArFL78ZfjJT+D3v88tL0rInb4+U0H+d7+DadOC\nlsYdMtaRUkq9D7PlyyeGX38E2KC1vjnhmN8C39BaPz/8+kng77XWf0z6LjEzxsl464m4KUuhIboP\nFtF/sIj+g0N0HyxO9J/NI+Vkn73kYxYMvzdmYQTvEP0Hh+g+WET/wSL6Dw7RvT9kW7U3ss+eUmoK\nZp+9h5OOeRj4GIBS6m1AVxTyowRBEARBEMZLRo+Uk332tNa/V0pdqZQ6CJwE/tpzqQVBEARBEEKA\nb3vtCYIgCIIg5BsFX9lcEARBEAQhV8SQEgRBEARByBExpARBEARBEHJEDClBEARBEIQcEUNKEARB\nEAQhR8SQEgRBEARByBExpARBEARBEHJEDClBEARBEIQcEUNKEARBEAQhR8SQEgRBEARByBExpARB\nEARBEHIk46bFbqKUkk39xonWWuV6ruh/fIjug0X0Hyyi/+AQ3QeLE/376pHSWuf8b8uWLQV9fpT1\nH7TuCln3+XC+G2zZsmXk37Zt2yL1+/0+f9u2baP05QZB/f6o6T75X5R1nw/nO8U3j1Q+0NfXxzPP\nP8PWx7bS0N7AwtKFXLf5Oja+YyNFRUVBixd50ul3YGAgaNGEYaL6DNx6661BizBu/NL9pk2b2LRp\n08jr2267zbXvLnSi+vyEgTDrTgwph/z8dz/n/r33c2zOMQaqBqAG6IcHHnyA+d+fz/qK9Tz03YeC\nFjOyXH/T9exu3W2r36IdRbzZ+aboN2Ay3SN5BrxFdB995B7mTth156sh9eKLL7JkyRLKy8vHfG7i\nDCkX0p0fi8Woq6sbeZ0sXywW44UXXqCRRnou7Bl98hQYWDRAPfWc2XWGp59+mmnTptn+xvHK7wZB\n6T/TubGhBH1uAAAbsklEQVRYjP379/Ncw3M0r28e/eGwfruHutl2cBv33nsvCxYsIBaLjRyybNky\nJk6cOPI6zLoHe/my4WfbB0be6+7upquri9OnT3PvvfeyvW47sUtio78k6Rk4cuQIixYtclV+N4hK\n3wOp+j9x4gTbDm2j7e1to7/Apv9ZvXp1aNt/GPueRP3Pnj2bnp54H3/27FlOnz7N/fffD0B5eTl1\ndXU0NTXR29tLWVkZJSUlLFu2jOLi4ox9T19fH7tbd1N/Yf1oIRLuIXvMcW57V2688UYA5s6dy1VX\nXTUmfQbd9t3ue7KN99u3b2f79u1j/JWg3IrDZr2QUrq2tpaWlhbbhz0IrEG8srJy5L1E+Swj6oUX\nX+Cuprs4u/hs2u+adHgS3934XTa+Y6Mnv1EphR5n0mFY9f/GoTe46dmbGKwZTHvsxMMT+VzV5+jp\n7GHjxo1UVlZy4sQJdu3axTvf+c6RByjMuvdKvlywa/u1tbUopVixYgU9PT0cOHCAo0ePsmrVKvbu\n38s/vflPDC0ZSvudkw5P4vYLbuevP/bXodR/WHQPY9P/qf5TfOPINxz1P8uXLg9t+w+z/js6Onj1\n1VdZt24ds2fPprGxkT/84Q+sXbuW4uJiWlpaePzxx1mwYAElJSUUFRVx7Ngxpk+fTllZGRdccAH9\n/f1pf9+jTzzKNQ9ew8Ci9GkKk+sn8/CHHuaKy68YeU/6Hvf6nmzjvR1O9e97+YPKykrq6+v9vqwt\ndXV1o5QKo+Wrq6tjcHCQvfV7OTs/fScGMDh/kMd2PJbyHWEjTLJZ+n9sx2MMVqc3ogDOzj/LU7uf\n4uKLL+bo0aOA6fzWrFmD1VFAuH6fHWGRz67tDw4OMmGC6RJaWlo4e/Ysy5cvp62tjT+89AeGFqTv\nyMA8A7tqd4Xi99kRFt3D2PS//eXtjvufMP3GZMIkW7L+m5qaWLFiBa2trQC88cYbrFmzhrY24wU8\nfPgwS5Ys4cyZMxQXF9PX10dlZeXI/Wpqasr4+7Y+ttWEpDIwUD3A1se2uvDr7AmL/oPqe7KN9+Mh\nkDpSQ0OZlRI0ifJprTl+8jhMyXLSFGjujoemwvwbwyZbc3ezI/12D3QDpKymSH4dtt+XTFjlS7dS\nRWtN++l2x89AWH8fhFf3kF7/HWc6xtT/hPk3hlU2S+/Z+halUp0Tifct3e9raG9wdA8b2hscSpwb\nYdZ/UH2PGzoJJNncsjzDSqJ8SinmzZgH/WS+mf1QNafK9jvCRthkq5pT5Ui/cybPAVI7s+TXYft9\nAPfcc8/I3+effz4bNmwIUBp7lFK2A4VSitJppY6fgfHqP9c8BSeEsW1YpNN/ydSSMfU/YfyNVvs/\nc+YMp06dCkXeViKW3rP1LXaDfeJ9S6f7haULHd3DyX2TPV1hGsa2AcH2PW7oxHdDyopJhoElS5ak\njZlan7e0tHBBzQU8fuzxzDkKxyaxeePmlO8IE/fccw+9vb2Ul5dz8uTJwDszS/+bL9nMb579TeYc\nqWMTec/697Br1y42btwIQElJyUiOlIUbuvdiIL/55puB8LQNu7Y/adKkkdlZZWUlnZ2dvPHGG6xa\ntYp3r3s3z735XOY8hWOTuPiCi6mpqRmXbF4tvw+L7mFs+t+0dhM7j+x01P+E6TcmcvPNN4cmRwdS\n9V9dXT2SIwWwfPnykRwpgMWLF4/kSHV1dY3KkbLOz6T76zZfxwMPPpA5R6ppMjffePOoHCk3S0+E\npW0E1fdkG+/Hg6/J5jfeeCPFxcXMmDEjpbMMilgsRn19PUNDQ0yYMIGampqUVXs7duzghu/ckLpq\nJoGq3VU8+P8epKioKOU7ciF5ML/tttvGnXS4a9cuV2Rzk1gsRm1tLe+/4/2pq/YSKHu+jK9f/3Wq\nq6tpb28fuV9Lly5l8uTJae+fG7iR8Llz507P5MsVu7YPjLzX09NDV1cXfX199Pf388VffDF15UwC\nVbur2PGdHSkrZ8aLG/qPSt8Dqfrv7Ozki7/4Yub+Z1cVP/uHn7Fy5UrpexySrP+ZM2fS29s78npg\nYIBDhw6NvC4tLaW+vp7GxkZOnTpFSUkJpaWlLF26lJKSkoy/r6+vj/M+el7qqr0EavbU8Np/vjZq\n1Z70Pe72PdnG+2Sc6t9XQ8qva3nB9Tddz+6W4ToW1QPGzdhvZhHzu+ezvtLbOhZuPFBh1n/Q+s1E\nvuveKUHdI9F/sM+H6N8dcrmHontD2PseMaQc0tAATz3VR9WCYCqrFsIDla1y7a5dUFcHH/iAv3IV\ngu4zoTXccQd88pMwdar/1YULXf8Wd95p+p9tL/nb/4j+DW1t8KtfwSc+kft3jLU6t+g+zqFDfdz3\nwDO0nAxf3yOGlEM++1n41regvx8mT/b/+vJAwebN8PjjMDQENnmJnlHoun/9dVi5Er7/fWNM+U2h\n6x/gyBGoqYHbb4dbbvH32qJ/w913w2c+A319MJwa5Tlu6D5xv8SwhLVz4ZOfhHvvNRM7r8g1rC1b\nxDjEKjXx5psQgny9gqRheGVwUxPMnx+sLIXEa6+Z///0p2DlKGReftn8L/cgOI4cMf83NsKyZcHK\nMhbyYZ9JgFOnzP+nT8O0ad5cI9eFLuFcCxlCGhuhpAQOHw5aksJEa2PMnn9+vEMT/KGhARYtik8m\nBP85eBAuuUTuQZA0Npr/m5qClaNQaWkZ/X+YEI+UQ5qbYd06eYiCor3duNOXL493aII/NDXB294W\n90wJ/nPkCLz97fBQRPe0TfSKRDW81NoKc+ZAR4d31/CyhlrUOX7c/N/ZacLcYUIMKQdoDbEYXHih\nGFJB0dICVVVQUWHuheAfVtt/6qmgJSlcjh2Dv/oruOce0x/5mSPoBvkQXmprMyE9Lw0pr2qo5QNt\nbXDuud7qP1fEkHJAby9MmmTCGwcOBC1N7kR5Vnj8OJSXm3/WzMQrZFY4mlgMrrkGurpgYCCYxRaF\nTksLLF4MU6bAiRMwe3bQEhUe7e1mQtHZGbQkhUlHB1x6KXR3By1JKr4aUlEdyDs7TX5UeTk8/bQ/\n1/RiMI/yrLCtDcrKoLTUJPx7iRezwqi2fTAdWHk5zJ1r/q6o8PZ6Xrf9qOkfTFhp3jzTD3V0eGtI\nyUQiFa2N3hctMhNrwV/OnDGTuMpKM5EIG1L+wAF79sBHPmKWv371q7Btm/8yFPoS5O99D159FS67\nDB55BP7rv/y7dqHrftUq2LrVhJYeesgk/PtJoesfYOZME97btAl+9CMY3rnEF0T/cPKkmch99asm\nX/auu/y5ruje0Npq+p3rrzf90ac/7c91nepfVu05oKsLiovNg9TeHrQ0hUlHh5mNW14RwT+6uoze\nS0tF90Fw5oypXzd7tumHurqClqjwsJ6BmTPD6RHJd3p6TKL/rFnm77AhOVIOsG5iaakJMQn+09Vl\nwkvFxeGMkecz1kTCCisJ/tLebnSvlLT/oLCegVmzohfai3pYG0ybnz3bGLInT3p3nVzD2mJIOcAy\npEpKJNEwKLq6zIoZGUj8pb8fBgdN6YmSEvHIBoHljQXTD0n795/ubqP7GTO8Hci9IMq5sRY9PcaQ\nmjHDW2eGFOT0EOsmWtsCWBVWBf+wZoRz5khow0+smaBSJrQhuvcfa7ELmHsRxtBGvhNlQyofsJwZ\nM2aYLXrChnikHGAZUhDP0ZEtSvzF6shmz5YcBT9JbvvikfWfzk4ziYDotv+oh5f8MqRkxaQ9iR6p\nMBqyYkg5oKfHxMYhPpiIIeUvyTHyoSGYIP5Uz7FmgmAG89raYOUpRKxEZzD9UBTDq1EPL/k1kEtB\nTntOnDBtv6gonIaUDEUOsG4iyKqxoLA6sgkTzMMUtYTPqJJY/FHy04LBCmtDeFct5TuWR6qoKJyh\npXzHcmYUFYUztUYKcjrgxAnjCQH/8kSkKOFoTpyIe0aswcSrooTiXo+T6I2VROdgsAZxMPcijDPy\nfCfsA3m+k+iRCqMhG5ghFSV6e1NDe17jdXXtqJE4oHu9BFnc63ESvbFRrmEU5UlEd7ep6AxmQue1\nN1YmEqn09JgteqZPD+dAnu+cOGF2VJg+PZyGrORIOSDRkCouloRbvxkaMrNwyys4a1b0Em6jOpAn\nGlJ+eaRke6TRdHfD8uXmbz8MKZlIpGKFuMUjFQzikcoDggjtCXFOnjQzkYkTzeuoG1JRItGQ8mvp\nvQzko0kO7UWt7ecDlkd86lRTW+3s2Xh/FHaiOolLxOqHvPYISkFOD+ntHW1IHT4crDyFRuJgDtGs\nLhxVgvBICaNJzAcM6/LvfMdavaoUTJtmvFLWmBB2ojqJSyTRkPLSI5jrJE4MKQdIaC9YEj2C4E94\nQzCcOAFVVeZvyyOltRlQBH9ILEExY0Y0237UvSKJxqwV3vPCkJL8NHv8MqRyRQwpByQO5LIE3H8S\nDVkQQ8pPEr2xkyaZ2XhivprgPYmDeFTbftS9IomLXbwczCWsbU/YDSmpI+WA5NCeeKT8JTm0Jzuw\n+0ey7mWLEv9JHMSj6pGKOn4ZUoI9Vj80ebJZfDQ4GLREoxFDKgtDQ+ahKSoyryW05z+JhiyIIeUn\ndoaUeGT9JTmsdOaMSXYW/CMxvCqGlP9Y/ZBS4dS/hPaycPKkmQVa25HMnRvdgSSqeQp2hlQs5t31\nJE8hjp0hJUasf2g9OrStVHwJeOJ9EbzDKr+S6JEK4xL8fEXr0f2QZUiFqf1LZfMsJCc6++WRklo6\nceySzevrvbue5CnEyZfQXhT7HjAD9pQpJj/Nwlq559VAIhOJ0fT2GuPVmkyH0SOSz5w5YyYQU6ea\n12HUv1Q2z4JdovOpUzAwYOK1XiGDeRxJNg+OfDSkokRibo6FtXG3V0jfM5rEsB6EcyDPZxL3+4Rw\negQltJeFZG/IhAnmoerqgvLy4OQqJOzqSEl4yR+S239UDamokjyIgySc+03yvp5RM6Si6o21SDak\nvKwuLwU5PSJ5EId4dXMxpPzhxAkoK4u/Fo+UfyR3YpIj5S/J+gcpyuk33d35Y0hFkWSvbBjLT4gh\nlYV0hpSs3POP3l6zYahFFA2pKM4KrRWrM2bE3/PDIyU5OnHsQntRNKSi2P4t/BzIpe2nkjwGh9GQ\nFUMqC8mhDRBDym/s6khF2ZCKCr29o1esgrkPHR3eXldydOLki0cqiu3fInGvQ/A2tCRtP5Uo5KhJ\nHaksiEcqeKSOVDDYeUMktOcvyfk5EM2JRJSJwkCez0QhtCqGVBbsZoRz53o/Kxfi5INHKorYJTpL\nsrm/BLFqTxhN8kBu1fES/CH5GQij/sWQyoLdjLCkRDxSfpIcXpVVe/5g1/bnzBFDyk/S5UjJRMI/\nkkN7YfSI5DNR0L8U5MzCiROwcOHo90pKoLnZ2+t6XZAzKvqHVK/g1KkmEbq/3xQrdBtJ+DR0d9uH\n9sSQ8g87r6B4pPylu3v0YpcwekTyGbvQatj0LwU5s5Ds1gUoLYV9+7y9rhdJh1HUP6TOypWKe6VK\nS92/niR8GpJnghBdQyqqk4jubliwYPR7skWSv3R1pSabh20gz2e6u6GyMv7ay2T/XJFVe1mwG0xK\nSiRHyk/s8tS8NKQEQzpDKop7TebLJAJkiyS/6e42W4NZhHEgz0RUJxEWyfr3MrQtBTk9Ip1Hqr09\nGHkKDWvD0OQSFJIn5T3pks2jaEhFleRBBKK5ajXKg3lXV6oh5ZVHSvZYTcXOI9ja6s21pCCnR9jN\nyktLoa0tGHkKjZMnzYMzceLo92VA956uLrNCNZE5c4zetTYhVsFb7PqfWbOil2we5cHcz9CeeANT\n8dOQzRVZtZcFu8GkrEw8Un5h5xEEqWfkB52dqd6QKVPMZt1h68jyFTtDKooeqSgThYE8n7HTf9gW\nW4hHKgvJNxFMjlRXF5w9m+opEdzFLkcE4p6RqBDF0EZnZ+ogDuZ56O4evXWMm0iycxy7/kfC2v7S\n2Tl6Mh3GgTyfSdb/jBnhM2TFkMqA1vYd2cSJZoDp6JCNi73GLkcEord6LIqhjc5OM2lIxjJiq6u9\nua6EN+LYecTFkPKPs2dNGDVxQhHFLXqijJ0hFbbQtoT2MtDbC9Om2dcqmjfP2yXIgsHOkAXzXleX\n//IUEh0d9qsiRff+YA3iUssrOKz8qMT9JqWOl3+cOWPqBSZ6v8NoyIohlYH2dvsZORhD6vhxf+Up\nROxyREAGcz/o6Ej1hoDo3i+6uozRNCGplxZDyj86OlLHgDAO5PmK5RVPXNgSRkNWKptnIJMhVVEB\nLS3eXVsqmxuS3boWxcVw7Jg315QcHUN7u1lYkUwU95qMYttP5xG0BpKhoVQjyw2k/cexGwOsZHNZ\nueo9dvoP416rUtk8A7FY+hyoykpvDSmpbG7IZEh5NZhLjg4MDhpvoJ3uo7jXZBTbfjqP4MSJxity\n4oS9t3a8SPuPYzeZmDjRpHzY1bcLI1GcRFjY6d/LHEEpyOkBQRpSgqGjw4RRkyktjd5gHiU6Ooyx\narcqVSr7+0N7e/r+Z86c1PpGYSaqg3lbm71X0BrM3TakpCDnaNra/DWkpCCnB7S2mhCeHdXVcOCA\nv/IUIu3tsHp16vslJVLLy0sytf2SEjhyxF95CpFYzD60CvE8tUWL/JUpV6I6mNsN5BAfzKuq3L2e\neANHY2fITptmPOZebVqfC5JsnoGWlvSDyYIF3uXoCHHa2+1nhFIU1VsyGVKyRZI/ZDKkohhejSKx\nmL1HfNYsSfj3Azv9KxW+BRdiSGWgqQnmz7f/7Jxz4OhRf+UpRNINJmVlUn7CS5qa0s+2Rff+cPx4\nemM2ign/UaS11d6QsorSCt5y/Lh9eDts+hdDKgONjekNqYULjSE1NOSvTIVGOs/IrFnGvRu2Crf5\nQnNzekNKaqj5Q7pBHIxXUAwp72ltNfmwyURtZ4Wokq4fsnIEw4LkSGXgyJH0OQjTp5tZYVOTCfMJ\n7qN1ekNKqXjC/5Il/ss2VqKWbHv0KCxbZv/ZvHne7b4Osvzeork5ffX4sjLZON0P0qV3SC01f2hp\nsTdki4vDFdoWQyoN/f1msDjnnPTHLF0KBw+KIeUVPT2mTo7dXntgZipNTdEzpKJAQwO85z32n1VW\nGpe7V3WMJOHWcOxYZkNKVg17z7Fj9lEJWeziD+n0HzaPrBTkTENdnTGQJk9Of8yKFVBbC178DCnI\nmTm0Ct4l/ItHBA4fhsWL7T+bMsUke8Zi6XN4wkbU2r7WxphN5xGvrIQ9e7y5trR/w5kzxuuUrvyK\nGFLeMjSUPk85bPqXgpxpOHAAVq7MfMz558O+fd5cXwpyZg6tgslT82IZfqF7RIaG4NAhOPfc9Mec\nc44xdKNoSEWB9nZTw2v2bPvPKyvNIOMFXvc9UTBkwbTv6mr7WmplZWay7TYygY5z/Lip01VUlPqZ\nV1u0SUFOl3n1VbjooszHrFkDW7f6I08hUleXOWy3ZAns3eufPIXCkSNmxpep2OCiRVBfD2vX+iZW\nQXHwoEkdSEfUyq9EzZAF0/+k88pWVHiTJygT6DiZvOIVFfDaa+5fM1f9y6q9NOzYARs2ZD5m7Vrj\nXj9zxh+ZCo3aWli+PP3nVmhVcJe9e423NRPnnmsGe8EbDhyAVavSf75woQn9yaph73jjjfQLLqz8\nTME7Mul//vxw6V8MKRtOnYKdO2HjxszHzZ5tOrudO/2Rq9D405/gggvSf37++WbQ19o/mQqB3buz\ne5pWroT9+/2RpxDZsyezR3zGDLNyKUyDSb7x2mv2uypA3JAVvGP//ujoXwwpG37zG+ONKi7OfuxV\nV8Gvf+29TIVGfz+88gqsW5f+mMpKU4bi0CH/5CoEnnkGLr008zFr1sAf/+iPPIXIjh1w8cWZj1m5\n0pvwhmB46SV461vtP5s3z9SwC1N17Xzj5ZfhLW+x/8xaMR+WSXRkDKnxJuA5PX9wEO64A266ydn5\nH/4w/Pd/Gy+WG9cPK+ORP5dzn3nGePuKizOf/653weOPu3/9MOFX2wezEu/VV0d7Y+3Ov+gik0vl\nZOWM6H9s57e1mZC1lVqQ7vy1a81g7/b1w4bffQ+YYpsHDkBfn/35EyY4M2QLWffjOb+/33jGBwft\nzy8uNkU5Dx/25vpjRQypBM6ehb/9W1OS/tprnZ2/bBlcdhn8y7+M//phxu/O7Nvfho9+NPv5118P\n992XeWZSyLof6/k/+IFp+4krZezOnzwZ/sf/cLbYQvQ/tvN/8hO4+mqzOWum89/1Lnj0UfevHzaC\nMKR+8Quj3x070p+/YQM8/7w31w8LQRlSjzwCF14If/xj+vPf9jZ49llvrj9WImNIeUlPj/EqrV8P\nb74JDz1kKmc75V//Fb73Pbj33vC4GqNKVxfccotJNLzxxuzHX3mlSbi94w5JvB0PWsPDD8Pdd8NX\nvuLsnM98Br72NbN6T3CHXbvgm9+Ef/zH7MdefrlZWfb0097LVUg0NMBtt8HnPpf5uGuvhfvvN94T\nwT3a2+FLXzJOjUxcd52Z+A0O+iNXJgq6/MFzz8H//t9mK4aNG+HLXzYPx1iMKDA1dbZtM54RwTl3\n3QVPPGE6ot5eUxekrQ3+/M/hqadM/lM2Jk6EX/7SeKa0djYACYa/+AsTkj5xwgzIZWXwq19lXnaf\nyKWXwhe+YPKlli413ql0y5WF0ezYAbffbtrs2bNw+rTph7q7zYTsvPOyf8eUKabPed/7jFH14IPe\ny50v3HGH6f/B3IOhIRgYMNWyDx0yhtSmTZDJoXH55Sb9YPlycy8//GE/JM8Prr46/rfW5t/goHFq\n7N9vUmuuuy5z6PSv/gr+679MVOjZZ4PdYURpn1woSinx1YwTrfUYTbw4ov/xIboPFtF/sIj+g0N0\nHyxO9O+bISUIgiAIgpBvSI6UIAiCIAhCjoghJQiCIAiCkCNiSAmCIAiCIOSI56v2lFLLgFuAX2ut\nf6OU+gwwG2jUWv97DudfCawB5mitvzAGOa4F3gXUaa3vHsN5bwX+J1AEfFlr3ef03HFed+R3A/3A\nWxjjb07+HtG/v/qPuu6HzxX9S9uXvidi+o+67ofPjYz+PfdIaa3fBH6S8FYHRrhpOZ7/Xq31PwP7\nlFIZdqNKoRfoASYppcbyuz8AbMEo9fIxnDeu6yb97stz/M2i/wD1nwe6B9F/4vnS9seA6F/aPgXS\n97jukVJKvRP4dMJb3wZGlg9qrR8YPu6zSqnFWuvDYzl/PHJorb+slPqfwDuBbWP9yrHKAKC1fhJ4\n0q/riv5H46f+81j35CIHiP6t78n3tg+i/2Sk7ZvvKYi+x+vyB0qpCuBLGEv4qxj34GqgGvi81npg\njOefN/wds7XWjssvDt/gDcBi4BatdafD894KXItxL34lB/dirte1fvd04BlgPmP8zUnfI/r3Wf9R\n1/3wuaJ/afvS90RM/1HX/fC5kdG/1JESBEEQBEHIEVm1JwiCIAiCkCNiSAmCIAiCIOSIGFKCIAiC\nIAg5IoaUIAiCIAhCjoghJQiCIAiCkCNiSAmCIAiCIOTI/wfQv3e4V0NbdAAAAABJRU5ErkJggg==\n",
       "prompt_number": 25,
       "text": [
        "<matplotlib.figure.Figure at 0x1ae172b0>"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Using Monte Carlo Methods"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pymc as pm"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "WARNING (theano.configdefaults): g++ not detected ! Theano will be unable to execute optimized C-implementations (for both CPU and GPU) and will default to Python implementations. Performance will be severely degraded.\n"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$$f(x \\mid \\alpha, \\eta) = \\frac{1}{\\pi \\beta [1 + (\\frac{x-\\alpha}{\\beta})^2]}$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "with pm.Model() as model:\n",
      "    th = pm.Uniform('th',lower=-pi/2,upper=pi/2)\n",
      "    alpha= pm.Uniform('a',lower=-3,upper=3)\n",
      "    xk = pm.Cauchy('x',beta=1,alpha=alpha,observed=x_samples)\n",
      "    start = pm.find_MAP()\n",
      "    step = pm.NUTS()\n",
      "    trace = pm.sample(300, step, start)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "c:\\Python27\\lib\\site-packages\\theano-0.6.0-py2.7.egg\\theano\\gradient.py:512: UserWarning: grad method was asked to compute the gradient with respect to a variable that is not part of the computational graph of the cost, or is used only by a non-differentiable operator: th\n",
        "  handle_disconnected(elem)\n",
        "c:\\Python27\\lib\\site-packages\\theano-0.6.0-py2.7.egg\\theano\\gradient.py:532: UserWarning: grad method was asked to compute the gradient with respect to a variable that is not part of the computational graph of the cost, or is used only by a non-differentiable operator: <DisconnectedType>\n",
        "  handle_disconnected(rval[i])\n",
        "c:\\Python27\\lib\\site-packages\\theano-0.6.0-py2.7.egg\\theano\\tensor\\subtensor.py:110: FutureWarning: comparison to `None` will result in an elementwise object comparison in the future.\n",
        "  start in [None, 0] or\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                5%                  ] 16 of 300 complete in 1.6 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                5%                  ] 17 of 300 complete in 3.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                6%                  ] 18 of 300 complete in 5.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                7%                  ] 21 of 300 complete in 5.8 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               8%                  ] 25 of 300 complete in 6.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               9%                  ] 28 of 300 complete in 7.9 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               9%                  ] 29 of 300 complete in 9.4 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----             10%                  ] 32 of 300 complete in 10.6 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----             11%                  ] 35 of 300 complete in 11.9 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----             12%                  ] 37 of 300 complete in 27.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----             13%                  ] 39 of 300 complete in 28.9 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----            15%                  ] 45 of 300 complete in 29.8 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [------           16%                  ] 49 of 300 complete in 30.3 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [------           17%                  ] 53 of 300 complete in 31.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-------          18%                  ] 56 of 300 complete in 32.9 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-------          19%                  ] 57 of 300 complete in 35.7 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-------          20%                  ] 60 of 300 complete in 40.6 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--------         21%                  ] 65 of 300 complete in 45.2 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--------         22%                  ] 67 of 300 complete in 46.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--------         23%                  ] 70 of 300 complete in 46.9 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------        24%                  ] 73 of 300 complete in 47.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------        25%                  ] 76 of 300 complete in 48.3 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------        25%                  ] 77 of 300 complete in 49.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----------       26%                  ] 80 of 300 complete in 50.9 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----------       27%                  ] 81 of 300 complete in 51.4 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----------       28%                  ] 85 of 300 complete in 52.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------      29%                  ] 88 of 300 complete in 52.6 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------      30%                  ] 91 of 300 complete in 53.7 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------      30%                  ] 92 of 300 complete in 58.9 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------      31%                  ] 94 of 300 complete in 59.4 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [------------     32%                  ] 97 of 300 complete in 59.9 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [------------     34%                  ] 102 of 300 complete in 68.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-------------    35%                  ] 107 of 300 complete in 69.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-------------    36%                  ] 108 of 300 complete in 80.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-------------    36%                  ] 110 of 300 complete in 81.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--------------   37%                  ] 113 of 300 complete in 81.8 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------------  39%                  ] 119 of 300 complete in 82.4 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------------  40%                  ] 120 of 300 complete in 83.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------------  40%                  ] 122 of 300 complete in 83.7 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------------  42%                  ] 126 of 300 complete in 84.3 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------------- 43%                  ] 130 of 300 complete in 84.8 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------------- 44%                  ] 133 of 300 complete in 85.3 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------45%                  ] 135 of 300 complete in 86.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------45%                  ] 137 of 300 complete in 88.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------47%                  ] 143 of 300 complete in 88.9 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------48%                  ] 144 of 300 complete in 90.2 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------48%                  ] 146 of 300 complete in 90.9 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------50%                  ] 150 of 300 complete in 91.8 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------50%                  ] 151 of 300 complete in 92.9 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------51%                  ] 154 of 300 complete in 93.9 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------51%                  ] 155 of 300 complete in 98.3 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------52%                  ] 158 of 300 complete in 98.9 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------53%                  ] 160 of 300 complete in 100.4 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------54%                  ] 163 of 300 complete in 101.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------55%-                 ] 166 of 300 complete in 107.2 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------56%-                 ] 170 of 300 complete in 107.9 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------57%-                 ] 172 of 300 complete in 108.7 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------58%--                ] 175 of 300 complete in 109.4 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------58%--                ] 176 of 300 complete in 110.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------59%--                ] 177 of 300 complete in 111.9 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------60%--                ] 180 of 300 complete in 114.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------61%---               ] 185 of 300 complete in 114.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------63%---               ] 189 of 300 complete in 115.2 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------65%----              ] 196 of 300 complete in 115.8 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------65%----              ] 197 of 300 complete in 116.4 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------67%-----             ] 201 of 300 complete in 118.8 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------67%-----             ] 202 of 300 complete in 120.8 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------67%-----             ] 203 of 300 complete in 172.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------68%-----             ] 204 of 300 complete in 178.6 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------68%-----             ] 205 of 300 complete in 180.3 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------68%------            ] 206 of 300 complete in 194.3 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------69%------            ] 207 of 300 complete in 222.4 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------69%------            ] 208 of 300 complete in 249.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------69%------            ] 209 of 300 complete in 252.3 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------70%------            ] 210 of 300 complete in 255.4 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------70%------            ] 212 of 300 complete in 290.9 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------71%-------           ] 214 of 300 complete in 292.2 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------72%-------           ] 217 of 300 complete in 293.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------72%-------           ] 218 of 300 complete in 293.8 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------73%-------           ] 219 of 300 complete in 294.4 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------73%-------           ] 221 of 300 complete in 295.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------75%--------          ] 225 of 300 complete in 297.4 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------76%--------          ] 228 of 300 complete in 298.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------78%---------         ] 234 of 300 complete in 298.9 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------78%---------         ] 235 of 300 complete in 300.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------78%---------         ] 236 of 300 complete in 300.9 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------79%----------        ] 239 of 300 complete in 302.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------80%----------        ] 242 of 300 complete in 305.4 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------81%-----------       ] 245 of 300 complete in 307.3 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------82%-----------       ] 247 of 300 complete in 308.2 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------83%-----------       ] 249 of 300 complete in 308.8 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------84%-----------       ] 252 of 300 complete in 323.8 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------84%------------      ] 254 of 300 complete in 324.6 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------85%------------      ] 255 of 300 complete in 325.6 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------86%------------      ] 258 of 300 complete in 326.2 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------87%-------------     ] 261 of 300 complete in 327.2 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------87%-------------     ] 263 of 300 complete in 328.3 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------88%-------------     ] 265 of 300 complete in 409.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------89%-------------     ] 267 of 300 complete in 409.7 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------89%--------------    ] 269 of 300 complete in 411.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------90%--------------    ] 271 of 300 complete in 411.7 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------91%--------------    ] 275 of 300 complete in 412.3 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------92%---------------   ] 278 of 300 complete in 412.8 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------94%---------------   ] 284 of 300 complete in 413.4 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------95%----------------  ] 286 of 300 complete in 415.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------95%----------------  ] 287 of 300 complete in 416.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------96%----------------  ] 290 of 300 complete in 416.8 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------97%----------------- ] 293 of 300 complete in 417.4 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------98%----------------- ] 296 of 300 complete in 423.4 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------99%----------------- ] 298 of 300 complete in 424.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------100%-----------------] 300 of 300 complete in 424.9 sec"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pm.traceplot(trace);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAA1kAAAEbCAYAAAAoDk59AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1ffc1070>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}